The England international joins after leaving Southampton upon the expiration of his contract, calling an end to an eight-year stay on the south coast.
Forster will act as an understudy to Hugo Lloris with loanee Pierluigi Gollini having returned to Atalanta after struggling to convince when handed starts in various cup competitions.
Spurs hope the 34-year-old will be the second of as many as seven signings under Antonio Conte this summer in an attempt to convince the Italian to stay long-term.
Ivan Perisic has already joined, also on a free, following the expiry of his Inter Milan contract. Inter Milan centre-back Alessandro Bastoni remains a key target, with talks under way over a deal which could reach £54million.
The club last month confirmed a £150m capital increase from Joe Lewis’ ENIC group in a significant boost to their transfer plans.