Mr Diamond is currently in charge of the corporate and investment banking divisions of Barclays, as well as the Barclays Wealth units.
From the beginning of October he will become the president and deputy group chief executive before taking over the top position from March 31st 2011.
Mr Varley will remain at the financial institution until September 30th 2011 in an advisory role on matters relating to regulation.
Marcus Agius, chairman of Barclays, thanked Mr Varley for his achievements at the bank and stated he was sure Mr Diamond would continue his successful work.
"I am delighted that Bob Diamond will be his successor. He is superbly qualified, with more than 30 years' experience in the banking sector, the last 14 of which have been with Barclays," he said.
Last month, the Wall Street Journal reported that Barclays Capital is to cut several hundred jobs in a cost-cutting measure after reporting a fall in revenue for the second quarter of the year.
By Tony Aynsley