After receiving his PhD, he applied successfully for an academic position at University of California, Los Angeles (UCLA).

Viterbi was later a professor of electrical engineering at UCLA and UCSD.
In 1967 he proposed the Viterbi algorithm to decode convolutionally encoded data.
It is still used widely in cellular phones for error correcting codes, as well as for speech recognition, DNA analysis, and many other applications of Hidden Markov models.
 On advice of a lawyer, Viterbi did not patent the algorithm.

Viterbi also helped to develop the CDMA standard for cell phone networks.

Viterbi was the cofounder of Linkabit Corporation, with Irwin M. Jacobs in 1968, a small telecommunications contractor.
He was also the co-founder of Qualcomm Inc. with Jacobs in 1985.
As of 2003, he is the president of the venture capital company The Viterbi Group.
He continues to be involved in wireless communications technology companies as a strategic advisor to Ingenu's board of directors.

In 1998 he was one of the few receiving a Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society.
Viterbi earned it for "the invention of the Viterbi algorithm".
 In 2002, Viterbi dedicated the Andrew Viterbi '52 Computer Center at his alma mater, Boston Latin School.
 On March 2, 2004, the University of Southern California School of Engineering was renamed the Viterbi School of Engineering in his honor, following his $52 million donation to the school.
He is a member of the USC Board of Trustees.

He is also on the Board of Trustees at The Scripps Research Institute.

He is also founding member of ISSNAF (The Italian Scientists and Scholars in North America Foundation).

In 2005, he was awarded the Benjamin Franklin Medal in Electrical Engineering.

Viterbi and Irwin M. Jacobs received the 2007 IEEE/RSE Wolfson James Clerk Maxwell Award, for "fundamental contributions, innovation, and leadership that enabled the growth of wireless telecommunications".

In 2008, he was named a Millennium Technology Prize finalist for the invention of the Viterbi algorithm.
At the award ceremony in Finland on June 11, 2008, he was awarded a prize of EUR 115,000 and the prize trophy "Peak" as a 2008 Millennium Technology Laureate.

In September 2008, he was awarded the National Medal of Science for developing "the 'Viterbi algorithm', and for his contributions to Code Division Multiple Access (CDMA) wireless technology that transformed the theory and practice of digital communications".

In 2010, he received the IEEE Medal of Honor and in the same year he also received the IIC Lifetime Achievement Award by the Italian Cultural Institute of Los Angeles.
In 2011, he received the John Fritz Medal from the American Association of Engineering Societies.

In 2013, Viterbi was inducted into the National Inventors Hall of Fame.

In 2017, Viterbi, along with Irwin Jacobs, received the IEEE Milestone Award for their CDMA and spread spectrum development that drives the mobile industry.
After receiving his PhD, he applied successfully for an academic position at University of California, Los Angeles (UCLA).
Viterbi was later a professor of electrical engineering at UCLA and UCSD. In 1967 he proposed the Viterbi algorithm to decode convolutionally encoded data. It is still used widely in cellular phones for error correcting codes, as well as for speech recognition, DNA analysis, and many other applications of Hidden Markov models.  On advice of a lawyer, Viterbi did not patent the algorithm.
Viterbi also helped to develop the CDMA standard for cell phone networks.
Viterbi was the cofounder of Linkabit Corporation, with Irwin M. Jacobs in 1968, a small telecommunications contractor. He was also the co-founder of Qualcomm Inc. with Jacobs in 1985. As of 2003, he is the president of the venture capital company The Viterbi Group. He continues to be involved in wireless communications technology companies as a strategic advisor to Ingenu's board of directors.
In 1998 he was one of the few receiving a Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society. Viterbi earned it for "the invention of the Viterbi algorithm".  In 2002, Viterbi dedicated the Andrew Viterbi '52 Computer Center at his alma mater, Boston Latin School.  On March 2, 2004, the University of Southern California School of Engineering was renamed the Viterbi School of Engineering in his honor, following his $52 million donation to the school. He is a member of the USC Board of Trustees.
He is also on the Board of Trustees at The Scripps Research Institute.
He is also founding member of ISSNAF (The Italian Scientists and Scholars in North America Foundation).
In 2005, he was awarded the Benjamin Franklin Medal in Electrical Engineering.
Viterbi and Irwin M. Jacobs received the 2007 IEEE/RSE Wolfson James Clerk Maxwell Award, for "fundamental contributions, innovation, and leadership that enabled the growth of wireless telecommunications".
In 2008, he was named a Millennium Technology Prize finalist for the invention of the Viterbi algorithm. At the award ceremony in Finland on June 11, 2008, he was awarded a prize of EUR 115,000 and the prize trophy "Peak" as a 2008 Millennium Technology Laureate. 
In September 2008, he was awarded the National Medal of Science for developing "the 'Viterbi algorithm', and for his contributions to Code Division Multiple Access (CDMA) wireless technology that transformed the theory and practice of digital communications".
In 2010, he received the IEEE Medal of Honor and in the same year he also received the IIC Lifetime Achievement Award by the Italian Cultural Institute of Los Angeles. In 2011, he received the John Fritz Medal from the American Association of Engineering Societies.
In 2013, Viterbi was inducted into the National Inventors Hall of Fame.
In 2017, Viterbi, along with Irwin Jacobs, received the IEEE Milestone Award for their CDMA and spread spectrum development that drives the mobile industry.
Andrew Viterbi