The 25-year-old is a holding midfielder capable of playing on the left wing. He has enthralled supporters of the French club with his ability to resist opponents, before quickly breaking on the counter attack.
Tainio, who was once on the verge of completing a move to Manchester United, will arrive on a free transfer in the summer.
"We are delighted that we have been able to secure Teemu now and do not have to wait until the summer to make the signing," said Frank Arnesen.
Nottingham Forest denied receiving a £4m bid for 22-year-old winger Andy Reid from Tottenham this week.
City ground chief executive Mark Arthur rejected a £5m bid from Tottenham for the rated Irishman last summer. Afterwards Reid was promised he could switch to any Premiership club that matched the club’s valuation.
Nottingham Forest are now facing a struggle to avoid relegation to the Coca-Cola League One under new manager Gary Megson.
Meanwhile, Spurs confirmed the 18-month loan signing of Egyptian forward Ahmed Hossam Mido from AS Roma and Excelsior's 20-year-old striker Mounir El Hamdaoui on a three-and-a-half year contract. The Moroccan striker is an immediate replacement for Edson Silva Sousa who joined Scottish Premier League side Hearts on trial earlier this month.