He said: "There has been talk about other clubs, but I never wanted out. This is what I have wanted all along.
"I know it has gone on for some time, but I am delighted we have finally reached an agreement.
Downing, whose decision came as manager Gareth Southgate finalised his preparations for Sunday's FA Cup fifth-round trip to Sheffield United, admitted the club's swoop for record signing Afonso Alves helped to make up his mind.
Southgate is delighted to have both men at his disposal as he builds for what he hopes will be sustained success.
He said: "I am sure it (Alves' capture) will have helped. All players want to see the club they are at are keen to improve and want to keep progressing.
"We can promise things and we can talk about doing things, but until we actually do them, then people will not believe them.
"As a club, we have made that investment and now we have followed up by agreeing with Stewart.
"He is still very young, really, and there is still lots of development to come.
"I still maintain at times, he does not realise how good he can be himself. He is a fantastic asset for us."