"I've been down that road a few times before and to be honest I panicked when I heard about it," he said.
"But thankfully we struck an agreement with Sylvain and I am really pleased we've got him.
"Last year when we showed an interest in him his price was £5m so to get him for free has got to be great business for the club."
He also denied Sol Campbell's place at the club may be under threat to make way for Distin.
"There is no way. Sol is still absolutely key for us. He has still a year to go on his contract and he's not going anywhere," he said.
"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."