Koeman did an impressive job during his two years at St Mary's and Puel will be looking to continue on and build on that foundation in the upcoming campaign.
The Frenchman has made six new signings and the Saints will be hoping for at least a top-10 finish again, even after losing some key players.
Southampton - 2016/17
Boufal is the club's record signing and is a skilful attacking midfielder from Lille.
Boufal scored 11 goals in Ligue 1 last season and he will be looking to chip in with a number in that region while creating plenty more for his forwards in his debut season in the Premier League.
Pierre-Emile Hojbjerg - from Bayern Munich for £12.75m
Having never played regularly at Bayern and making only a handful of appearances in the senior side, Hojbjerg now has a chance to make a name for himself at Southampton.
At just 21, he has already starred for Schalke having spent last season their on loan, making 23 starts.
Hojbjerg will be hoping to establish himself within the side and continue to develop as an exciting young midfielder.
Winger Redmond has been snapped up from Norwich City who were relegated to the Championship last season.
He is a pacy and tricky wide man who featured 36 times in the Premier League in 2015/16 and netted six goals in his highest talley of his career so far.
The England U21 regular has a fierce shot and can be deployed on either wing, but will mainly be deployed on the right side of the centre-forward.
At 22, he is primed to take the next step and has already scored this season on his debut for the club in their 1-1 draw at home to Watford.
McCarthy has been signed to compete with number one goalkeeper Fraser Forster who is currently sidelined with an injury.
McCarthy was also recently called up to replace Forster in the England squad and he may well challenge him both at international and domestic level to claim the starting jersey.
Pied is a French right-sided midfielder/full-back who played under Puel at Nice.
Unfortunately, Pied went down with a serious knee injury in late August and is likely to be sidelined for the majority of the season.
Stuart Taylor - unattached for free
Taylor is the third piece of the goalkeeping puzzle and will deputise behind Forster and McCarthy.
At 35, has enough experience at senior level to step in take over if the aforementioned pair are crocked.
Played three times in the Championship for Leeds United last season.
Redmond is a decent signing and will impress but a striker was needed to replace Pelle who moved to China, and Wanyama's presence in midfield will be a miss as Hojbjerg isn't of that mould.
As a result, the Saints may struggle to reach the heights they experienced under Koeman if the new brigade do not fire.
Pied's unfortunate injury compounds their below par summer dealings.
Tribal's Transfer Rating: 6/10