The Ivory Coast international was released by Manchester City earlier this summer after a tumultuous past two seasons or so in which he was banned for six months after taking a prohibited diet pill.
This lead to Toure becoming just a squad player at City but now he is looking forward to reigniting his career at Anfield.
"Liverpool have given me the chance to show that at 32 I'm still one of the best defenders, and I will fight for that," said Toure who is now officially a Reds player.
"These past two years of being 'part-time' have helped me refresh and be more hungry.
"I want to try and help Liverpool win trophies this season."
He added: "It's like coming to a new school. But as soon as I came, Steven Gerrard came up to me and told me that if I needed anything, I could come to see him - that shows the spirit and mentality of this club.
"The manager (Brendan Rodgers) welcomed me when I came, and all the players as well.
"It's really important to be part of a team that has spirit and togetherness and that's what I see here. For a first day, I'm really happy."