The French midfielder has been on loan at the Giallorossi since January and the Roman outfit have been keen to make his move permanent.
Dacourt has established himself as a key member of Fabio Capello's side and he has signed a three-year deal at the Stadio Olimpico.
The deal had stalled as both clubs failed to agree a fee, but a compromise of £3.3 million has now been reached.
Roma had originally agreed to pay £4 million for the former Everton star, but they insisted on a reduced fee for the Frenchman's signature.
Leeds officials met with their Roma counterparts over the weekend and the Elland Road club have confirmed they have accepted Roma's revised offer by faxing the Italian club.
"We spoke on the telephone and confirmed the terms we had discussed in London during the last few days," said Roma's director of sport Franco Baldini.
Leeds have officially stated that there are still a few minor details to thrash out, but Dacourt is on his way to the Italian capital on a permanent basis.