Chilean Pellegrini, who replaced Roberto Mancini as City boss last summer, secured the award for the first time after guiding his side to a seven-match unbeaten run during the month.
City won six of their seven Premier League games in December - they only dropped points in a 1-1 draw at Southampton - including important home victories over title rivals Arsenal and Liverpool.
The 60-year-old claimed the award ahead of three other nominees, Manchester United boss David Moyes, Chelsea manager Jose Mourinho and Everton's Roberto Martinez.
Brendan Rodgers, Arsene Wenger, Mauricio Pochettino and Alan Pardew are the four previous winners this season.
Suarez was named the Premier League player of the month following his record-breaking goalscoring streak during December.
The Uruguay international failed to find the net in the 3-1 defeat at Hull at the start of the month but he then hit a purple patch starting with a four-goal haul in the 5-1 demolition of Norwich at Anfield.
He followed that up with two goals in each of the next three games against West Ham, Tottenham and Cardiff to become the first player to score 10 goals in a calendar month in the Premier League.
Suarez won the award ahead of Manchester City stars Alvaro Negredo, Vincent Kompany and Yaya Toure.
England and Everton starlet Ross Barkley was also nominated along with Arsenal's Theo Walcott, who has subsequently been ruled out for the season.
Suarez, the Premier League's top goalscorer, said: "It's so important when you work hard on the pitch and they recognise it when you win these prizes.
"On the pitch I try to help Liverpool and I try to help the squad and I think also for the confidence it is very good.
"If Liverpool continue in this level we can finish in the top four, which we want."