Nani, full name Luis Carlos Almeida da Cunha, was at Manchester United for eight seasons and has since spent one season each at Sporting, Fenerbahce and Valencia.
The 30-year-old has made 112 appearances for Portugal scoring 24 goals.
Lazio, fourth in Serie A last season, have spent modestly during the transfer window, with new signings totalling 17 million euros ($20 million), according to the specialist website Transfermarkt.
($1 = 0.8412 euros)
(Writing by Brian Homewood in Berne; Editing by Mark Potter)