Mr Baker will take up his appointment in February 2018.
Foreign Secretary Boris Johnson said:
The UK is at the forefront of diplomatic work with the Libyan government and our international partners to help bring stability to Libya. If left unchecked the violence and ungoverned space will only increase the challenges from illegal migration and terrorism. These are issues that matter to the people of Libya, but also to people here in the UK.
Frank has served the UK well as our ambassador to Iraq and also Kuwait. I look forward to working together with him to help Libya make progress towards the political solution and more secure future it so deserves.
Commenting on his appointment, Mr Baker said:
I am honoured to be the new British Ambassador to Libya. Britain and Libya have a long history.
Over the coming weeks I will listen to and learn from people across Libya and discuss how we can work together to achieve our common interests.