The Portsmouth manager spoke of his relief at having beaten off interest from several Premeirship sides including Liverpool who had moved in with a late bid.
"Thankfully we struck an agreement with Sylvain and I am really pleased we've got him," Redknapp said.
"Last year when we showed an interest in him his price was five million (pounds) so to get him for free has got to be great business for the club.
"I have been an admirer for a long time. He's a fantastic player, left-sided and good in the air and very powerful."
Distin said it had been a tough decision to leave the club.
"I was five years at Manchester City and made a lot of friends there," said the Frenchman.
"But you have got to have ambition and for me that means trying to push for Europe. Portsmouth are capable of doing that, more than capable, and that's why I am here.
"When you are on a free transfer you are going to get a lot of offers but this is the one I wanted to take," Distin added.
"Harry Redknapp was a big influence. I like the way his teams play and this is definitely a club on the way up."
Campbell to stay
Distin, who cost $8 million when he joined the Blues from Paris St Germain in 2002, could soon be joined by Ghana midfielder Sulley Muntari, currently playing with Italian side Udinese, who is expected to be Redknapp's next summer signing.
Redknapp meanwhile dismissed rumours that Sol Campbell, last season's major transfer coup, could be shipped out to make way for his new signing.
"Sol is still absolutely key for us. He has still a year to go on his contract and he's not going anywhere.
"I will try, in fact, to sign another defender very soon because you have to have competition for places and a big squad.
"The Premiership is going to be tougher than ever next season and if you stand still you end up going backwards."
Other transfer targets
Redknapp's other targets are Titus Bramble, released after five years at Newcastle, and Middlesbrough's out of contract Australian striker, Mark Viduka, who is mulling over an offer from Portsmouth.
"Mark will make up his own mind. He has plenty of offers but we are looking to improve all around," Redknapp said.
"We will need more goals and we have the money available to spend. The chairman is ambitious."