The European Commission has cleared the deal and said it did not raise competition concerns because Fox and Sky are active in different markets in Europe.
It is now up to UK regulators to decide whether the deal would result in Fox owner Rupert Murdoch controlling too much of the British media. Last month, culture secretary Karen Bradley referred the takeover to Ofcom and the Competition Markets Authority after highlighting media plurality concerns.
Ofcom is investigating whether Fox is a "fit and proper" owner of Sky, while the CMA is reviewing jurisdiction issues.
As well as Fox’s 39% ownership of Sky, Murdoch’s News UK owns Times Newspapers, publisher of The Times and The Sunday Times, and The Sun/The Sun on Sunday publisher News Group.
Six years ago, before Fox and News UK owner News Corp were split, News Corp’s bid for a Sky merger was thwarted by the phone-hacking scandal at The News of the World newspaper.
In a statement following today’s decision, Fox said: "21st Century Fox welcomes today's decision by the European Commission clearing unconditionally its proposed transaction to acquire the outstanding shares of Sky that it does not already own.
"We now look forward to continuing to work with UK authorities and are confident that the proposed transaction will be approved following a thorough review process."