Godman was released by Edinburgh after finding his No.10 shirt filled by converted scrum-half Greig Laidlaw, who also took his place in the international pecking order for Scotland.
Laidlaw's outstanding performances helped guide Edinburgh to the quarter-finals of the Heineken Cup for the first time in their history as Godman looked on in frustration.
Godman has won 23 caps for his country and has joined the Exiles, coached by Simon Amor.
And the 29-year-old believes the move south is the perfect way to kickstart his career.
Godman: "I'm excited to be joining a club with such a prestigious history. Obviously, with its Scottish heritage, it was a definite attraction for me.
"After a few injuries recently, I'm looking forward to kick-starting my career and getting on the pitch for London Scottish."
Scottish, playing in the second tier of English rugby, hold the record for producing the most Scottish internationals and Godman is the third Scot they have captured in a short space of time.
Amor added: "A core part of the London Scottish philosophy is always being on the lookout for Scottish talent. The signing of Phil's calibre not only fits into this philosophy, but his quality shows the ambitions of the club as we prepare for a second year in the Championship."
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