Ford is expected to join the side in February before the three-match T20 International series against India.
The news was announced in Surrey county's website as they confirmed their current coach Ford's decision to leave for international assignment.
Ford had earlier coach Sri Lanka for two years starting from 2012.
Ford coach Surrey since 2014 and helped the club gain promotion back to the First Division of the County Championship and guided them to the final of the one day championship also.
"It was a very tough decision for Graham to leave Surrey but we understand that the opportunity to go back and coach at International level with Sri Lanka was too good to turn down. Despite the timing of his decision, we wish Graham all the best and we will immediately start our search for a new Head Coach," Stewart announced.