At the same time, Beasant headed to the south coast to solve Brighton's goalkeeping problems while Brannan joined Scottish side Dunfermline on loan for the rest of the season.
Bullard, 22, is a player who Paul Jewell has been tracking for the best part of a year.
Until now, Peterborough have refused to sell despite interest from several clubs.
But with the finances tight at London Road, the Posh decided to cash in and do business.
Preston North End had an undisclosed bid turned down last week while Stockport County saw a cash and player swap deal rejected.
Bullard started his career in non-league football at Gravesend before being snapped up by West Ham in 1999.
But having failed to break into the first-team squad at Upton Park he joined Posh in May 2001 on a free transfer. He's an attacking midfielder with an eye for goal, having found the net 11 times in 62 league games at Peterborough.
On the outgoing front, Brannan's departure to Dunfermline is not too much of a surprise as he has struggled to be part of Jewell's plans.
The 31-year-old started the season at right-back but made only seven starts.
He's no stranger to Scottish football having spent more than two years at Motherwell before Bruce Rioch brought him to Wigan in February 2001.
Brannan joins former Latics team-mate Derek Stillie at East End Park and the loan deal may become permanent if he impresses Pars boss Jimmy Calderwood.
Much more of a shock is Beasant's move to Brighton and he was today putting pen to paper on a contract with the Seagulls for the remainder of the campaign.
The veteran keeper only joined Latics in October but a clause in his contract allowed him to leave.
Jewell said: "We've unfortunately lost Dave but we had an agreement with him that if another club showed an interest to take him permanently, then he could go.
"Brighton have lost their loan keeper Ben Roberts through illness and tried to get Dave last week but we managed to hold them off.
"They came back in this week and the move suits him because Brighton is on his doorstep more or less, and at 43, he wants to play.
"He's been good to have around the place and we wish him well down there."
Jewell says he is unlikely to bring in another keeper unless John Filan gets injured, and 17-year-old Ryan Yeomans will be back on the bench for tomorrow's home game with Cheltenham.
Lee McCulloch is forced to miss the clash through suspension, with Peter Kennedy likely to be shunted forward to the left-wing with Steve McMillan coming in at left-back.
While it's top versus bottom tomorrow, Jewell has warned that the game will be no stroll for Latics.
"Cheltenham went to Cardiff a couple of weeks ago and were unfortunate to beat beat 2-1.
"It won't be easy and I imagine they will come here and made things difficult for us.
"Some people might look at this game and say it's three certain points for Wigan, but that is certainly not the case.
"We might have 40 odd points more than Cheltenham but come 3.00pm it won't make any difference."
Article from the Wigan Evening Post.