The Italian striker has joined the Saints from Feyenoord, where he played under former Dutch international Koeman for the last two seasons.
Pelle scored 50 goals at almost a goal-a-game for the Eredivisie outfit and later followed his former manager, who succeeded Mauricio Pochettino in the close season, to St Mary's.
"Koeman and I worked together for two amazing years at Feyenoord, and I hope that it will be the same here," said the 28-year-old Italian.
"I had some teams interested in me, but this is going to be the best choice for me because the club wants to keep improving every year.
"The talks between us were only short in terms of how long it took to convince each other because I was pretty sure that, for me, this would be a great step."
Southampton surprised many by finishing eighth in the Premier League last season, a performance that left an impression on Pelle.
He added: "Last year, everyone in Europe was impressed by the performances of the team, and it's clear that the club is growing.
"The Premier League is amazing, and Southampton is showing year-by-year that it wants to improve."