Quaife-Hobbs graduated to GP2 last season after winning the 2012 Auto GP title.
The 23-year-old Briton began his rookie campaign with MP before making a mid-season switch to Hilmer and winning the reverse-grid race at Monza.
He joins team returnee Simon Trummer at Rapax.
"After a successful rookie year in the 2013 GP2 season I am looking forward to returning this season to fight for the championship," said Quaife-Hobbs.
"Together with Rapax I feel we can have a winning season."
Rapax driver Stefano Coletti was a title contender early in 2013, as three wins gave him the championship lead.
But he faded as the season went on and ended up only fifth in the standings.
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- Simon Trummer