And he was recently linked with Aberdeen and St Johnstone.
Accies manager Billy Reid told his club website: "I'm pleased to make this signing as I think his style of play fits ours perfectly."
Hamilton say they faced competition from other Scottish Premier League clubs for McAlister's signature.
The midfielder joined Morton from amateurs Linwood Rangers in 2002 and has been linked with a number of clubs since becoming a first-team regular in 2004.
In 2008, when manager of Motherwell, Aberdeen's Mark McGhee admitted his interest in signing McAlister, but it appeared that the Fir Park club were unwilling to match Morton's valuation.
Then, in August, McAlister took up an invitation from coach Dan Petrescu to have a trial with Unirea but afterwards said that he would prefer to remain in the UK.
Following a training stint soon after with Watford, manager Malky MacKay said he would be monitoring McAlister's progress.
However, the winger finished the season just passed still at Cappielow, although he missed the final six games after breaking a bone in his foot in April.
In his absence, Morton escaped relegation with a final-day comeback to defeat Ayr United 2-1.
The Greenock club have, though, since sacked manager James Grady and assistant Allan McManus.
Ryan McGuffie this week joined First Division rivals Queen of the South, while fellow midfielder Erik Paartalu has left to join A-League outfit Brisbane Roar, as their contracts expired.
Now Hamilton have given McAlister a chance to prove himself in the SPL.
Source: BBC Sport