It is believed that Bolton were paid £300,000 by City to enable the move.
"We have agreed compensation with Bolton," said Pearce. "I think they will be reasonably happy with that and we have a top quality player.
"First off all, I thought Didi would still be a Liverpool player and not available, but then his agent phoned me and my first thought was to make sure everything was clear at Bolton.
"We have to be seen to be whiter than white in a situation like this. That's why I rang Sam Allardyce and he gave me permission to talk to Didi.
"I am delighted he is here as he brings experience and leadership qualities to the team. He has everything.
"If you get more winners like him in your squad, you are going in the right direction."