Mr Brasher, who took on the role around a year ago, has stepped down from the board with immediate effect and will leave the company in July.
Philip Clarke, who is currently Tesco's group chief executive, will then take over responsibility for UK operations.
Mr Clarke said: "I have decided to assume responsibility as the CEO of our UK business at this very important time.
"This greater focus will allow me to oversee the improvements that are so important for customers."
Tesco issued a profit warning in January after recording poor Christmas sales, sending shockwaves through the supermarket industry.
Mr Clarke said the announcement "categorically does not signal another warning" and insisted he had not had a row with Mr Brasher.
He added: "The UK's been facing challenges that are long standing.
"This is a consequence of my wish to take a more active role in the day to day management and nothing else, and Richard recognising you can't have two captains in a team."
Sky News City editor Mark Kleinman, who exclusively revealed the move on Wednesday night, said: "What this all adds up to is a sign that all is not well at Tesco, which has really been the dominant force in British retailing for the last 15 years.
"After Christmas, it announced that it had had its worst festive trading period in about 20 years and investors in the city reacted very badly to that, wiping £5bn off the company's market value in a single day."
Earlier this month, Mr Brasher announced Tesco is to create an extra 20,000 jobs in the UK over the next two years.
He told Sky News: "In unprecedented economic conditions like these, major businesses have a big responsibility to step forward, invest and create jobs."
Mr Brasher insisted the pledge will be borne out, despite accusations that major supermarkets are inflating employment creation numbers.
He said: "We are not counting people who move around our business... These are real net new jobs, and that's what we stand behind."
Mr Clarke also paid tribute to the work Mr Brasher had done at the UK's biggest retailer.
He added: "He will leave behind a UK business which has very strong plans for improvement and, over the last two months, these plans are beginning to show progress, in line with our expectations.
"I am more determined than ever that these improvements in the UK will result in a better Tesco and an even better shopping trip for customers."