Ramsey scored the Gunners’ second after Diego Costa cancelled out Alexis Sanchez’s opener as the north Londoners denied Premier League champions Chelsea the double with a 2-1 win.
They had started their final against the Blues as clear underdogs after a disappointing season, finishing fifth and missing out on Champions League qualification for the first time in Wenger’s nearly 21 years in charge.
But a fourth-minute goal from Sanchez and a pinpoint header from Ramsey in the 78th did not tell the whole story as they dominated Antonio Conte’s conquerors.
Ramsey says: “I can’t describe this. It’s been an up and down season. We’ve finished with the FA Cup so it has to be successful.
“I’ve got the winner again [after his 2014 clincher over Hull]. I love this competition. The boys deserve this.
“I’m happy for the manager. To get another FA Cup – delighted.
The midfielder adds of Wenger: “Of course I want him to stay at club. He deserves this.
“We changed the formation and had a lot of success.
“Fair play to him, he changed the system. Hopefully, he’ll be there next season.”
It was Wenger’s seventh Cup success – a record as he more than doubled the club’s tally from six to a record 13th in his time at the club.
And without giving too much away about his plans for the future at the club, the Frenchman says he is proud of his achievements.
He explains: “I am very proud because nobody has done it. It’s not easy.
“I’m especially proud of the way we won this time because we had to play against Manchester City in the semifinal here and then Chelsea here. You cannot get tougher.
“We had two outstanding performances so this Cup was won with special spirit and special attitude.”
Commenting on his future, the 67-year-old says: “It would be a bit ridiculous that 20 years depend on one game and that the future of the club depends on one game. We’ll know more next week.”