He has signed a three-year contract and becomes Latics' second summer signing after the capture of goalkeeper Mike Pollitt a week ago.
Manager Paul Jewell is relieved to have brought to an end a frustrating time in the transfer market and hopes more signings will follow shortly.
And he's delighted to have landed a player of Chimbonda's quality as he prepares for life in the top flight.
Jewell told the Evening Post: "Pascal is a great player and it's a real boost for us to have completed this signing.
"We beat off competition from Marseille to land him and that says something about the calibre of player we now have.
"Pascal is just what we need at the back, he's strong, quick and versatile, and is equally at home at full-back or at centre-back.
"I have no doubt he will be a major asset to us in the Premiership and he will fit into the squad of players here and with the kind of football I like to play.
"Hopefully getting Pascal will change our luck in the transfer market.
"We have worked hard all through the summer to try and bring people in, the phone has never stopped ringing.
"I've asked people to be patient when it comes to making signings and that is now paying off."
Latics' pursuit of Chimbonda has dragged on for the best part of a fortnight since he became available following Bastia's relegation from the French top flight.
Initially, West Ham, Nancy and Marseille were also interested, but the player set his heart on a switch to the Premiership.
And the path became clear for Latics when the Hammers dropped out of the running.
Last weekend a fee of around £500,000 was agreed with Bastia but Jewell later cooled his interest when the asking price went up.
But the clubs got back round the negotiating table earlier in the week and thrashed out a deal.
Chimbonda travelled to Wigan on Wednesday night to meet Jewell, and then successfully completed a medical at the JJB yesterday.
In the meantime, his agent Willie McKay met with Latics' football co-ordinator Bill Green to discuss personal terms.
At one stage it looked like the talks would drag on until today, but an agreement was reached just before the close of business last night.
All that was needed to be done today was for the deal to be registered with the FA and the transfer money moved to Bastia's account.
Jewell is now working on further deals, and he hopes to bring another four players to Wigan before the big kick-off.
Wolves striker Carl Cort is reported to be a target, although Molineux have denied receiving any bid from Latics.
Meanwhile, Gareth Whalley is set to sign for Swindon.
The midfielder was released by Latics at the end of his contract in May, having played nine times for the club last season. Another former Latics player on the move is goalkeeper Derek Stillie who has joined Dundee United from Dunfermline.