Koeman beat Crystal Palace's Neil Warnock, Leicester City's Nigel Pearson and Chelsea boss Jose Mourinho to scoop the Manager of the Month award, while Pelle has been named as the top flight's Player of the Month.
The Saints, who were tipped for relegation at the start of the season, grabbed wins in all three of their league fixtures last month, while Pelle found the back of the net three times.
"It's a great compliment," Koeman told the club's official website. "It's a personal prize for the manager, but I have to say thanks to the players it's always those on the pitch who win games.
"We had a great month, which was maybe unexpected for a lot of people and maybe that's had an influence on this prize.
"Everybody was a little afraid before the season, but we've done a great job – all of the coaches and the technical staff, and all of the people at the club."
Pelle added: "I'm really happy. I'm proud of myself, but it's not just about me. Thanks go to the staff, my teammates and all of the supporters because we are all together.
"I'm really happy in general with what I've been doing over the last couple of years. I believe that this is the most beautiful job in the world, and I am enjoying it a lot."
Koeman secured 39 out of 40 of the votes from the panel, while Pelle earned his award by receiving just one vote more than Leicester's Leonardo Ulloa.