The Belgium international right-back has agreed a two-year contract at the Stadium of Light and is available on a free transfer after leaving Lille at the end of his deal.
Sunderland have moved quickly to see off competition for the 34-year-old. Meunier had been in talks with Valencia over a move to Spain, while Hull City had also opened discussions, but the Black Cats have won the race for his signature.
The defender arrives fresh from this summer's World Cup, where he made three appearances for Belgium before their elimination at the hands of Spain.
Meunier brings a wealth of top-level experience to Regis Le Bris's squad as they prepare to add a Europa League campaign to their Premier League commitments next season. He began his career at Club Brugge before spells at Paris Saint-Germain, Borussia Dortmund and Trabzonspor, racking up more than 300 club appearances, and spent the past two years in Ligue 1 with Lille.
His signing follows the template Sunderland used to such good effect last season, when experienced heads Granit Xhaka and Reinildo Mandava proved invaluable alongside the younger core of the squad during the club's return to the top flight.
On Wearside, Meunier is expected to provide competition and cover for Trai Hume and Nordi Mukiele on the right side of defence, with his ability to operate further forward offering Le Bris additional flexibility.
Provided there are no late complications with the medical, the move is expected to be completed and announced within the next 24 hours, allowing the veteran to join up with his new team-mates ahead of Sunderland's opening pre-season friendly away at York City.
More business is expected to follow on Wearside, with the club continuing to work through a list of targets across several positions as they gear up for a first European campaign since the 1970s.