The 43-year-old, who worked under Jones with Japan and later England, was the strong favourite to take up the position after the Australian's sacking and leaves his role as head coach of Premiership club Leicester Tigers.
"I'm deeply honoured to be appointed England head coach and I am very excited by the challenge," said Borthwick, who has signed a five-year contract with the RFU.
"The English game is full of talent and I want to build a winning team which makes the most of our huge potential and inspires young people to fall in love with rugby union the way I did."
Reuters reports former Saracens and Bath lock Borthwick, who made 57 test appearances for England and retired from playing in 2014, was the forwards coach of the national team from 2015 to 2020 and gained a reputation as an exciting young mentor in the game.
He then took over as Leicester's head coach and guided the club to the title in the 2022 season, after they came second-bottom in 2020. The team are currently fifth in the standings and unbeaten in the European Champions Cup after two games.
Known for his attention to detail and for being the polar opposite to Jones, who had a difficult relationship with the media during his spell, Borthwick will take charge for the first time in England's Six Nations opener against Scotland on Feb. 4.
Jones's tenure ended earlier this month following a review of their November series that ended with England being booed off the pitch at Twickenham Stadium after a humbling 27-13 defeat by world champions South Africa.
That result came after a draw against New Zealand, a win over Japan and a defeat by Argentina, completing a year in which England won only five of their 12 tests.
Borthwick's longer-term focus will be on the 2023 World Cup in France as England look to build on their runners-up finish to the Springboks in Japan three years ago.
His coaching team will include Kevin Sinfield who has been appointed defence coach, taking on the role this week.