Ings joined Liverpool after being at his clinical best and impressing during Burnley’s first season back in the Premier League in 2014/15.
Ings showed early signs of promise under previous manager Brendan Rodgers following his move to Liverpool, who paid an initial £6.5 million to the Clarets after a tribunal.
However, the Englishman was unlucky with two serious knee injuries from which he is still recovering, having made only 25 appearances in all competitions in three years.
Ings will leave Merseyside to join the south coast club on a season-long loan ahead of a permanent move on July 1 next year.
Liverpool have managed to return a significant profit on Ings, receiving £18 million up front, with an additional £2 million in add-ons. The two sides have also agreed on a 20 percent sell-on clause.
Ings will be hoping that he can shine at Saints under the leadership of Mark Hughes as he looks to revive his career and start afresh.
For Klopp, sanctioning the move was something he reluctantly agreed to, praising the 26-year-old to LiverpoolFC.com following the move:
“It is a very strange feeling saying goodbye to Danny. The biggest emotion is how much we will miss him,” Klopp said.
“He is such an outstanding boy. Honestly, if you could bottle character and spirit, his would sell worldwide—he is so incredibly positive and full of energy.
“But we won’t just miss his character because he is a footballer who has all the tools.
“So we say farewell to a friend, but for Danny I know the best chapters in his personal story are still to be written.
“He is as fit now as at any point of his career I would bet and he just requires the opportunity.
“He has that opportunity and on behalf of his Liverpool family we say good luck Danny and we will miss you.”