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Sturridge, who joined Liverpool from Chelsea in January 2013, leaves having scored 67 goals in 160 appearances in all competitions for the Merseyside club.
Moreno was signed from Spanish side Sevilla in August 2014 and represented Liverpool on 141 occasions.
"The most important words to say to these two remarkable players is 'thank you'," manager Juergen Klopp, who guided Liverpool to their sixth European title on Sunday, told the club's website.
"They were here when I arrived as manager and during that period they - as much as anyone - helped to establish us as a team that would be heading in the right direction.
"Without them we wouldn't be the team and club we are in this moment... we will miss them of course, but we can say farewell with the best words possible: guys, you leave as European Champions."
Klopp said Sturridge, who spent a spell on loan at West Bromwich Albion in the 2017-18 season before returning to score four times last season, could be considered a "modern-day Liverpool great."
"He came to the club while we were trying to rebuild and re-establish ourselves. Some of the goals he has scored for Liverpool were so important," the German added.
"What maybe is missed on the outside of the club by many is what a great leader Daniel is in our dressing room... he's been great with many of the younger players also, so he's been so important to our progression here."
Moreno lost his place at left back in the first team to James Milner and Andy Robertson and played only five times last season but Klopp hailed the 26-year-old's professionalism.
"Maybe the minutes on the pitch he would have wanted and deserved were not there, but his contribution didn't diminish. How he was in training kept the entire group on their toes," Klopp said.
"Albie is world class and I know he will be back in the Spain national team in the not too distant future."
Liverpool finished the Premier League season second behind Manchester City before beating Tottenham Hotspur 2-0 in the Champions League final.