Wanyama has joined Tottenham from Premier League rivals Southampton in the summer transfer window.
Former Tottenham and Rangers defender Roberts has backed the defensive midfielder to be a success at White Hart Lane.
Wanyama joined Southampton from Scottish Premiership giants Celtic in the summer of 2013.
The Kenya international defensive midfielder soon established himself as a key figure in the Saints’ team and as one of the best in his position in the Premier League.
The former Beerschot midfielder scored one goal and created 15 chances in 30 Premier League matches for Southampton last season.
Wanyama had a pass accuracy of 82% and a shot accuracy of 21%, and won 64 headers, 23 dribbles and 71 tackles.
Tottenham enjoyed a successful 2015-16 Premier League campaign and will feature in the Champions League next season.