Downing had been linked with a move to Tottenham in January's transfer window - but after no move came about, the club opened new talks with the England wideman.
Downing told the club's website: "This is where I want to be.
"It's my hometown club but I had told them that I didn't want us to stand still. Signing Alves shows how ambitious we are.
"There's been talk about other clubs but I never wanted out. This is what I've wanted all along.
"I'd like to thank the fans for the support they have given me.
"They could have really got on my back in recent weeks in response to all that was being said. But they have been great."