As director of communications for NHS England, Enright, 51, has been at the forefront of managing the communications around the coronavirus pandemic.
As well as leading a 30-strong national team for the body that shares out £100 billion of annual NHS funding, commissions healthcare services and sets the priorities of the NHS, he is also understood to manage media relations for Sir Simon Stevens, the NHS chief executive.
Before joining NHS England in 2013, Enright spent 16 years working for the BBC, where he rose up the journalistic ranks to become the deputy editor of Newsnight.
The son of the late Labour MP and MEP Derek Enright, who represented Hemsworth and Leeds in the 1980s and 90s, Enright once defended the BBC against claims it was acting like the "thug at the end of the street" in its dealings with local and regional newspapers.
Insisting the corporation was not trying to monopolise the local news market, he told a Westminster Media Forum event in 2013: "I think there is a simple BBC argument which, certainly when I worked at Newsnight and the 10 O'Clock News, is that all competition is good.
"I hear people saying they are worried about the BBC entering local space. It is a mixed picture for me. Are you saying we are crap, or good and dangerous?"
A former BBC colleague described the Oxford-educated married father of three, who is chairman of governors of the St Charles and St Mary's Catholic Schools Federation in Ladbroke Grove, London, as "the dream person to be in this role".
The former colleague added: "He's a really positive, likeable person. He'll be straight, enthusiastic and open with colleagues. This is a very smart hire at a time when the Prince of Wales could do with some help."
Enright, who is due to take up his post in May, will replace former BBC and Burberry PR chief Julian Payne as Charles's director of communications after Payne announced in January he was leaving to become chair of corporate affairs at Edelman.
During his five years in the role, Payne, 48, is credited with improving the prince's public approval rating by spearheading positive coverage including a well-received BBC documentary to mark his 70th birthday in 2018.
The Duke and Duchess of Cambridge have also recruited a new press secretary from the NHS.
Victoria O'Byrne, the director of communications for Test and Trace, starts at Kensington Palace in May. She has been in charge of communications for the heavily-criticised £22 billion programme for seven months and previously spent two years working for the Lawn Tennis Association, where she is likely to have come into contact with its patron the Duchess.
She is also a governor of School21 in Stratford, east London, which the Cambridges visited earlier this month, days after the Sussexes' interview, when Prince William declared: "We are very much not a racist family."