The 39-year-old will become the club’s 20th manager in their 120-year history but their fourth in the last two years.
He will bring with him assistant Colin Pascoe, performance analyst Chris Davies and head of sports science and medicine Glen Driscoll.
Swansea were looking for between £4 million and £5m to compensate them for the loss of Rodgers, who only signed a new three-and-a-half-year contract in February.
In addition there was some additional negotiation by the Welsh club over recompense for the loss of their other staff. That has now been successfully concluded and Rodgers will officially take up his position today, when he will hold a press conference in the Anfield trophy room.
Owners Fenway Sports Group will hope the Antrim man will lead the club into a new era after the chopping and changing which has taken place in recent times.
The appointment of Rodgers signals the start of a restructuring the football side of operations and further details are expected to be revealed at today’s press conference regarding the Americans’ ideas about the roles of sporting and technical directors, considering Rodgers was not keen to cede control of football matters to a higher authority.
Former Liverpool striker John Aldridge believes Rodgers’ style will be appreciated by players and fans alike at Anfield.
“He’s done absolutely fantastic at Swansea,” Aldridge said.
“Some people will say that his lack of experience will go against him but you have to start somewhere in your football life and this could be his time.
“I think [Rodgers] and Swansea were a breath of fresh air last year and if he can bring that to Liverpool and win a lot of games percentage-wise and bring top European football to the table he’ll be a king around the place.”
Meanwhile, Wigan have confirmed assistant manager Graeme Jones has been given permission to talk to Swansea about replacing Rodgers.