The Hammers stopper has shone since he joined the Saints at the end of March - keeping two clean sheets in four games to help pull them out of the bottom three.
And with regular number one Kelvin Davis still sidelined with a dislocated finger, Wright is needed more than ever as the Saints look to avoid the drop to League One.
Manager Nigel Pearson told the club's official website: "I am delighted Richard is able to stay until the end of the season. He has done well for us and has enjoyed his football.
"He has made some outstanding saves and has looked confident and composed and he had been a big presence for us while Kelvin has been sidelined."