The Imps have been looking for a new keeper following the breakdown of talks with Rob Burch over a new contract.
Anyon is manager Chris Sutton's third signing of the summer, after Mustapha Carayol and Josh O'Keefe.
Former Walsall midfielder O'Keefe, who like Anyon came through the youth ranks at Blackburn Rovers, signed a two-year deal with the Imps.
Winger Carayol, 20, also agreed a two-year deal with Lincoln after turning down a new contract at Torquay.
As he is under 24 Torquay will be entitled to compensation for the Gambian.
Source: BBC Sport
Source: BBC Sport