The former West Ham United striker makes the short trip to Ipswich and joins on a two-and-a-half-year deal.
Murphy is the league's top scorer with 17 goals, while McGoldrick has bagged seven this term.
Sears isn't the most prolific of scorers himself, but he has been the outstanding player in a relatively poor Colchester United team.
The 25-year-old burst onto the scene in 2008 when he scored the winner on his debut for West Ham against Blackburn Rovers.
Following a few loan spells in the Football League, he moved on a permanent deal to Colchester in 2012. The 25-year-old scored 34 goals in his two-and-a-half years a the club.
Sears will add some depth to the side, and while unlikely to displace the aforementioned just yet he gives McCarthy another option from the bench. He leaves Colchester in desperate need of a replacement, however, and they will need to act quick.