The duo, who join as a senior creative team, will report to Nik Studzinski, the executive creative director at Publicis, and will be working across the agency's portfolio of clients.
The pair began working together in 1997, after TBWA merged with Simons Palmer Denton Clemmow Johnson. They then switched to Partners BDDH, where they became board-level creatives before a merger with Euro RSCG in 2003.
Studzinski said: "I'm delighted that Steve and Matt are joining us here at Publicis. They are a talented and passionate team with a track record for producing great work, and they are a fantastic addition to the creative department and the agency."
Nicholls added: "To work on great brands and household names such as McVitie's, Vicks, KP and Cadbury is an opportunity that we are both excited about.
"Nik Studzinski shares the same passion for good creativity as we do, and is also one of the industry's good guys. The chance to join Publicis was just too good to ignore."
Before he began working with Nicholls, Anderson spent time at Simons Palmer and Saatchi & Saatchi. He started his career at Dorland in 1984.
Nicholls started his career at TBWA Holmes Knight Ritchie in 1994.