Reuters
The BBC and other news outlets confirmed with the Foreign Office that Barrow, a senior diplomat, will play a key role in the UK's Brexit negotiations.
Rogers unexpectedly quit his position on January 3. He was expected to renew his position when his 4-year-term expires in November so that he could play a leading role in talks between Britain and the EU.
His shock resignation meant that many feared that the UK government lost one of its most experienced and knowledgeable negotiators just weeks before withdrawal talks get underway at the end of March.
In a 1,400-word word resignation letter, published in full by The Telegraph, Rogers called on former colleagues to challenge "muddled thinking," and "ill-founded arguments," and called for them to "speak truth to power." He adds that "serious multilateral negotiating experience is in short supply in Whitehall."
You can read the full letter here.