The 32-year-old has made 373 appearances for the club, winning two Premier League titles and the Champions League as a key member of the side that restored the Reds to the top of the English and European game under Jurgen Klopp.
However, he has dropped down the pecking order this season since the arrival of Milos Kerkez and his contract, which expires at the end of the campaign, will not be renewed.
The Scotland captain is the second high-profile departure from Liverpool in the coming months after Mohamed Salah announced he will also depart at the end of the season.
“I’ll always look back on amazing memories at this football club, I’ve put my heart and soul into the club for nine years and I’ve not got many regrets,” said Robertson.
“I’ve grown as a man and as a person. This club will always mean the world to me, the fans will mean the world to me. It has been a hell of a journey.”
Less than a year on from winning the Premier League, Liverpool have endured a miserable campaign, marked by tragedy off the field.
A close friend of Robertson’s, forward Diogo Jota died in a car accident in July.
On the field, Arne Slot has struggled to find the right balance from an expensively assembled squad that sits fifth in the Premier League.
Liverpool were also dumped out of the FA Cup 4-0 by Manchester City last weekend and lost 2-0 in the first leg of their Champions League quarter-final against Paris Saint-Germain on Wednesday.
Robertson’s rise was one of the success stories of Klopp’s glorious reign at Anfield.
Signed from relegated Hull for £8 million ($11 million) in 2017, he quickly became a fan favourite.
He sits behind only former team-mate Trent Alexander Arnold as the defender with most assists in Premier League history.
On top of Premier League and Champions League glory, Robertson won the FA Cup, two League Cups, the Club World Cup and UEFA Super Cup.
“I’m still fully focused on trying to end this season as positively as possible, to help these lads and to try to give a few more good moments to the fans,” added Robertson.
“That’s my aim and hopefully then we can do it and maybe closer to the end of the season you’ll have me down a camera crying my eyes out.”