England striker Sturridge, 29, scored 67 goals in 160 appearances after joining from Chelsea in January 2013.
Liverpool manager Jurgen Klopp said: “The most important words to say to these two remarkable players are thank you.”
Klopp hails amazing outgoing Liverpool duo
The Reds are keen to offer Klopp a new contract after winning the Champions League with a 2-0 victory over Tottenham in Madrid on Saturday.
The German said: “Alberto is a person whose personality is reflected in how he plays – full of life, full of energy, always positive. An unbelievable character who is always willing to give all of himself for the team.
“Daniel has earned the right to be considered a modern-day Liverpool great, I would think. 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, so, so important.
“We will miss them of course, but we can say farewell with the best words possible: Guys, you leave as European champions.”
Both players leave Anfield having fallen out of favour during the 2018-19 season. Sturridge made 27 appearances in all competitions but 20 of those were as a substitute. Moreno made just four starts and one substitute appearance.
They were both part of the Liverpool team that was beaten in the 2016 EFL Cup and Europa League finals in Klopps first season in charge.
Sturridge began his career at Manchester City before joining Chelsea in 2009. He also spent six months on loan at Bolton during his time at Stamford Bridge before making the move to Anfield.
He scored 24 goals in his first full season at the club as Luis Suarezs strike partner as Liverpool challenged for the Premier League before ultimately finishing second to Manchester City.
After struggling for first-team football he spent the second half of last season on loan at West Brom, although injury restricted him to just six appearances.
In November 2018 Sturridge was charged with misconduct by the Football Association over alleged breaches of betting rules in January of that year. The striker, who denies the charges, was given until February to provide written evidence but has yet to hear a verdict from the governing body.
Moreno, who has been capped four times by Spain, came through the youth ranks at Sevilla before moving to Anfield for around £12m. He was first-choice left-back left for two seasons but lost his place to James Milner and then Andy Robertson in recent seasons.
Sturridge with his goals, especially in those amazing first few seasons, and Moreno with his antics. Because he may not have been the best left-back to wear the colours, but he was one of the more colourful characters around the dressing room.
And that’s how he should be remembered. We’ll always have that picture of the mad unit nipping out with his dog while riding a hoverboard, and we’ll always have that time Moreno beat Kammy at his own game live on air.
The Spaniard was asked to recreate Kamara’s catchphrase at the press conference before a Europa League game against Villarreal after he was heard saying it following the incredible 4-3 win over Borussia Dortmund.
And he just about manages to get it out before giggling and looking left and right for moral support. But don’t worry Al, we got your back. We got your back.
The 26-year-old joined Liverpool from La Liga outfit Sevilla in August 2014 for £16.20 million, according to Transfermarkt.co.uk, and went on to make 141 appearances with three goals and 11 assists.
Moreno was eventually forced out of first team reckoning through a combination of injury, Andy Robertson and James Milner. As Robertson has emerged as one of the finest left-backs in Europe there is no shame in that.
Back in March the Spaniard was linked with a move back to his homeland with Barcelona, while Lazio have also been rumoured to be interested in the player.
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