Arsenal Ladies' bid was "reluctantly accepted" by their fellow Women's Super League One side in January.
The Gunners activated a release clause in Oshoala's contract, subject to her gaining a work permit for 2016.
Oshoala, 21, was named the BBC's Women's Footballer of the Year in 2015.
She is presently in Zurich as a panellist at the Fifa Women's Football and Leadership Conference 2016 and is expected in London on Wednesday to finalise her switch to the two-time FA Women's Super League champions.
Oshoala joined Liverpool ahead of the 2015 WSL campaign but injury blighted her time at the club and she only scored three goals in 12 league outings last season.
The first player from Africa to compete in the Women's Super League, Oshoala burst into the limelight when she emerged as the leading scorer at the 2014 Under-20 World Cup in Canada and was voted the tournament's best player.
Her performances led Nigeria to the final, where they were narrowly beaten by Germany, and she was also a major influence in the senior Nigeria team, who won a record seventh African Women's Championship in October 2014.
That ensured their qualification for last summer's Women's World Cup in Canada, where Oshoala scored her only goal of the competition in a thrilling 3-3 opening match against Sweden.
But the first player to win the BBC Women's Footballer of the Year award, voted for by football fans around the world, could not stop the African champions from exiting the tournament in the group stage.
Nigeria international striker Asisat Oshoala has been granted a UK work permit, clearing the path for her to complete a switch to Arsenal Ladies from rivals Liverpool Ladies.