Manchester City's youngsters finished off a job well done against Leicester City, adding to their 3-0 first-leg lead with two late goals from Isaac Buckley and Brandon Barker at the King Power Stadium. Layton Ndukwu had given Leicester hope of clawing back the advantage with 20 minutes to go but substitute Buckley and Barker struck to kill that dream off and set up a final against Chelsea later this month. City will face Chelsea at a venue, likely to to be the City Football Academy Stadium, in the first leg on April 20 before travelling to Stamford Bridge a week later on April 27. Manchester City's Isaac Buckley Ricketts (left) celebrates scoring at the King Power Stadium on Wednesday . Manchester City's players celebrate after they consolidated their first leg lead to reach the Youth Cup final . Leicester City: Smith-Varnham, Miles, Chilwell (c), Choudhury, Kipre, Johnson, Bailey (Barnes 62), Fox, King, Rowe (Muskwe 72), Ndukwu . Unused subs: Knight, Bramley, Dombrauskis, . Bookings: Choudhury . Manchester City: Haug, Maffeo, Humphreys, Oliver, Angelino, Bryan (c) (Bullock 92), Nemane, Wood (Buckley 46), Celina, Garcia, Barker . Unused subs: Albinson, Fernandes, Dilrosun . Bookings: Wood, Bryan, Angelino . With City holding a big advantage from the first leg last month, this clash always looked difficult for Leicester, and their inability to find an early goal made the task of overhauling the advantage even tougher. City were the better team for much of the first half but goalkeeper Kjetil Haug had to be aware to keep out Hamza Choudhury from close range at the other end. That was their best chance until Charlie Oliver handled inside his own penalty area with 20 minutes to go to gift Ndukwu the chance to give the home side the lead. That opportunity was one he gratefully accepted, confidently dispatching his spot-kick past Haug. Layton Ndukwu of Leicester City scores from a penalty to cut the deficit but it was not Leicester's night . Brandon Barker (right) scored City's second goal of the evening as they made it to a first final in seven years . Despite still holding a decent lead, City surged forward in response and Buckley equalised, thumping home Barker's cross. And Buckley effectively returned the favour when he was hauled down inside the area moments later to allow Barker to make it 5-1 on aggregate from the spot. City march on and face Chelsea in a rematch of their last final in this competition seven years ago. The Premier League champions' youth side won 4-2 on aggregate on that occasion and will be hoping for a repeat this year. Manchester City's  Barker (right) in action with Leicester City's Hamza Choudhury (centre) in midfield . Keenan King battles for the ball with City's Charlie Oliver, who gave away a penalty with 20 minutes to go .
Manchester City reached FA Youth Cup final with win over Leicester City .
Substitute Isaac Buckley scored to cancel out Layton Ndukwu opener .
Brandon Barker added a second in stoppage time to win the game .
Chelsea are their opponents in the final, having beaten Tottenham 5-4 .
Two-leg final takes place on April 20 and 27 with City at home first .