Costa claimed the EA Sports Player of the Month award with two goals and two assists as Chelsea won three straight matches against Everton, Middlesbrough and Tottenham Hotspur to extend their winning run to seven consecutive Premier League victories.
This meant Conte was rewarded with his second successive Barclays Manager of the Month award.
Pedro received the Carling Goal of the Month award for his curling strike in the 2-1 win against Spurs.
Costa and Conte claimed their awards after receiving the most votes from a panel of experts, Premier League captains and the public were combined.
Pedro also came out on top after a combination of votes from a panel of experts and the public, who voted via the Carling Tap.
The Premier League 2 Player of the Month award went to Josh Sims, the Southampton winger.