Roberts has signed an initial six-month contract at the Stadium of Light, yet there is a club option to extend the deal following the conclusion of the 2021-22 season.
It became clear at the start of the transfer window that Sunderland were tracking Roberts after his availability became known.
The playmaker was on loan at French club Troynes but made just one senior appearance in Ligue 1.
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Roberts signed a long-term contract at City in 2015, which was due to end this summer, meaning negotiations weren’t straightforward, while the player was also recovering from Covid.
The 24-year-old was surplus to requirements at the Etihad Stadium and made just three appearances for the current Premier League champions amid several loan spells.
Roberts will be remembered fondly for his loan spells at Celtic, while he has also played for Middlesbrough, Derby and Norwich in recent years.
The player will now be keen to settle at a club as he tries to help Sunderland win promotion from League One.
Roberts told Sunderland’s official website: “I can’t wait to get going. I came to the game against Sheffield Wednesday a few weeks ago to get a feel for it and it was great to watch – and something that I wanted to be a part of.
"The fans want you to do well and work hard every matchday and that pressure and expectation is something I thrive off. I just want to do well for the people that support me and get Sunderland back to where they belong.”
Roberts becomes Sunderland’s third signing of the window following the arrivals of right-back Trai Hume and centre-back Danny Batth.
Batth, who has moved to Wearside on an 18-month contract from Stoke, is expected to come straight into the side to face Portsmouth this weekend.
Sunderland head coach Lee Johnson was keen to add another playmaker to his squad, even though Alex Pritchard and Elliot Embleton have performed well in recent weeks.
On Roberts’ arrival, Johnson added: “Patrick is a player that we have always kept our eyes on over the years because he really is a top talent.
"This is an amazing opportunity – for him and the club – to give him the love he requires at a standard whereby we think he can excel and then come with us to the next level.
"He thrives on the big occasion and the beauty of Sunderland is that there is a big occasion every three days. We hope that this is the place he calls home for a number of years.”
Sunderland are still hopeful they can make more signings before the end of the transfer window, with another striker the priority.
Jermain Defoe has spoken about the possibility of returning to Wearside after leaving Rangers, yet the 39-year-old has multiple options as he considers his future.
Sunderland’s squad also appears light at right-back and in central midfield due to long-term injuries.