The Netherlands international, who can play along the right flank, has penned a five-year contract after Liverpool activated a €35 million (£29.5m) release clause.
The Reds' move to snap up Frimpong quickly comes with the knowledge of Trent Alexander-Arnold departing Anfield to join Real Madrid.
The 24-year-old is now expected to compete for the right-back slot with Northern Ireland defender Conor Bradley, who recently penned a new four-year deal.
"Liverpool came and said they had interest, and obviously for me it was a no-brainer," Frimpong told Liverpool's official website.
"For me, it was like, 'Whatever you guys do, just get this done', (speaking to) my agents: 'Just get this done'.
"Liverpool fans, I'm going to give my all, my energy, my work-rate and hopefully we can win together, we celebrate together, get everything together.
"I'm just excited to be here. Thank you guys for accepting me and I won’t let you guys down and I’ll give you the energy that you guys want."
Frimpong's career started as a youth player at Manchester City before joining Celtic in 2019, then moving on to Leverkusen in January 2021.
He emerged as a key figure at Leverkusen under Xabi Alonso, helping the club win the Bundesliga unbeaten last season and the DFB-Pokal.
Frimpong made 190 appearances in total for Leverkusen, recording 30 goals and 44 assists during his stint in Germany.
Frimpong's former club Celtic are said to be owed a portion of the transfer fee, with Sky Sports reporting the figure could be worth around £5 million.
Liverpool are also showing an interest in Frimpong's former teammate Florian Wirtz and, according to The Athletic, have made a €130 million (£109.4m) bid to sign the playmaker.
Wirtz has already snubbed Bayern Munich this summer, while Manchester City have pulled out of the running for the 22-year-old.