The striker was secured from Queens Park Rangers in January.
The striker joined in a cut-price deal from Queens Park Rangers last month, with them moving quickly to secure on the cheap.
He made an instant impact at St Mary’s as well, with a headed goal against Manchester United securing all three points for his new side on his debut.
And Rodriguez says he is looking forward to linking up with his former Burnley striker once more when he returns from injury.
“I was made up when we signed Charlie and he's the best buy of the window,” Rodriguez told the Sun.
“I was surprised no one else went in for him. His record speaks for itself. He's a goal scorer and he's done well. Southampton did well to get his signature and it's great business. He's a brilliant player.”
“It will be great to rekindle the partnership. We had a good relationship at Burnley which is important, we complimented each other.”
The Saints will now be hoping that Austin could add some goals to the side as they hunt down European football next season.
With the open nature of the league this season, they are firmly in the race for a place in the top six come the end of the season.
Competition is fierce though, with goal difference likely to prove a key factor, and Southampton will be keen to see Austin scoring regularly in the thirteen games left to secure their place in their top six.