The Belgium international has put pen to paper on a three-and-a-half-year deal at the City Ground until the summer of 2027, and Forest could fork out up to £5m for his services.
Sels will compete with Matt Turner, Odysseas Vlachodimos and Wayne Hennessey for the Garibaldi gloves, and he reinforces Nuno Espirito Santo's goalkeeping department following the permanent exit of Ethan Horvath to Cardiff City.
The 31-year-old returns to England having previously turned out for Newcastle United from 2016 to 2018, helping the Magpies win promotion back to the Premier League in his debut season, although he played just 14 times for the club in all tournaments and spent the 2017-18 campaign on loan at Anderlecht.
Sels ended his underwhelming St James' Park stint with a permanent move to Strasbourg five and a half years ago, and the 6ft 2in shot-stopper has represented the Ligue 1 club on 175 occasions, keeping 42 clean sheets in the process.
In each of Strasbourg's first 19 top-flight games of the 2023-24 season, Sels wore the captain's armband in between the sticks, and he has one major honour to show from his time at the Stade de la Meinau, winning the Coupe de la Ligue in the 2018-19 campaign.
After earning his first Belgium call-up in 2015, Sels finally made his Red Devils debut in 2021 and has since played six times for his country, including four appearances in 2023 thanks to Thibaut Courtois's ACL injury.