Rodgers, who will be officially presented at a press conference on Friday morning after a compensation package was agreed with Swansea, worked as part of Mourinho's staff when he was in charge at Chelsea.
Mourinho told The Sun: "I am very happy with his appointment at Liverpool, especially because he did it as a consequence of all his amazing work at Swansea.
"Brendan is a good man, a family guy and a friend.
"When he joined us at Chelsea he was a young coach with lots of desire to learn.
"But he was also a coach with ideas, who was ready not just to listen but also to communicate and share."