The midfielder got the all-important goal in the 74th minute after pinball in the Stoke area, with team-mates David Silva and Mario Balotelli also involved.
Manchester City 1 Stoke 0: Yaya the hero again as Blues end 35-year wait for trophy
Matchwinner: Yaya Toure holds the FA Cup aloft after his goal won the trophy for Manchester City
Toure said: 'The dream is now... It's fantastic to win. It's fantastic for the history of the club.
'We wanted to win something and get through to the Champions League. It's amazing.'
Manager Roberto Mancini, whose side also secured Champions League football next season with a 1-0 win over Tottenham at Eastlands on Tuesday, was equally delighted with the victory and wants his side to build on this success.
'I can say only that I'm very happy for all the supporters,' said the Italian. 'After many years they deserve to win this trophy.
'I didn't feel we dominated this game. We need to improve but we are very happy. We did a small piece of history of Manchester City. We start now.'
Striker Mario Balotelli was named man of the match and said: 'I'm happy. I said to the guys before the game "we're better than them, we have to respect them and give everything and if we do we're going to win".'
Asked if it was his best performance of the season, he said: 'All my season was s*** - can I say that? I've played not very well, but today maybe I played more for the team.'
Drinks are on me: Mario Balotelli (left) was named man of the match
Goalkeeper Joe Hart was not interested in questions about rivals Manchester United's taunts over City's lack of silverware before today.
'I couldn't care less that they do at Old Trafford,' said the England international. 'It's nothing to do with Manchester United, it's about Man City.
'We deserved to win the cup, we've beaten the best and we've beaten a very good Stoke side today.'
Defender Micah Richards was lost for words after City's triumph.
He said: 'It's unbelievable. Words can't describe it. We've worked hard all season. Now it's happened, it's unbelievable.
'This is the first one and this is the most important. We've got to build on this.'
Midfielder Adam Johnson added: 'Take a little look at what it means to the fans - 35 years of wait and we did it.'
Double act: Adam Johnson (right) celebrates Toure's winner
Stoke goalkeeper Thomas Sorensen admitted Manchester City deserved their victory.
The Dane said: 'They played the best stuff on the day.
'It's disappointing that we didn't play better. We've done so in the past - especially lately, we've done really well - that's the most disappointing thing.'
Sorensen, whose opposite number Hart made a fine save to deny Kenwyne Jones shortly before Toure's winner, felt the goal came just at the wrong time.
'I thought we were coming back,' he added. 'The first half was a big disappointment - we never really got playing.
'I thought they were running out of ideas so it came at a bad time for us. We were just getting into the game. We'd just had a good chance with Kenwyne. We're just so disappointed.'
?Manchester City 1 Stoke 0: Yaya the hero again as Blues end 35-year wait for trophyLIVE: Manchester City end 35-year wait for silverware with FA Cup triumph over Stoke - as it happenedExclusive: The nine-year-old rebel who became City's ideal Kompany manAll the latest Manchester City news, features and opinion
?Explore more:People: Joe Hart, Adam Johnson, Roberto Mancini, David Silva, Thomas Sorensen, Mario Balotelli Places: Manchester, United Kingdom
Source: Daily Mail
Source: Daily Mail