The deal is pending a physical, after which Liverpool can discuss terms with Suarez.
The agreement brings to an end negotiations that have lasted for weeks. Ajax had set a midnight deadline on getting a deal done.
The £22.8 million transfer fee breaks a club record, set with Fernando Torres in 2007, who cost roughly £20 million ($31.6 million).
Suarez was excited about a potential move to Liverpool, saying that he wanted to go to England to follow in the footsteps of fellow South American superstar Carlos Tevez.
“[The Premier League] is a league that attracts me, a country where the football is really good,” Suarez told the Sunday Times. “Alongside [La Liga] it is the best in the world. In England you have a lot of clubs with aspirations to become champions and they are also very strong in the Champions League at the European level. … I think it’s a kind of football that suits me.”