Shepherd will start on the 35,000 sq ft development at Wellington Place next month.
The £5.5m contract will take twelve months to complete and the five-storey building marks a new stage of development at the Wellington Place site.
MEPC Chief Executive, Rick de Blaby, said: “Construction of 10 Wellington Place marks the start of the next phase of development, with planning permission granted for a further 300,000 sq ft of office space here in the heart of Leeds’ West End.
“Like MEPC, Shepherd is a long-established company which has become an industry leader by delivering the highest levels of quality and by working closely with its clients at all stages.”
Colin Sargeant of Shepherd Construction said: “As well as delivering much-needed high quality new office space in Leeds city centre, this scheme is a landmark development for Leeds, which will also create excellent retail facilities on the ground floor and a new public square.
“More importantly, 10 Wellington Place will mark a turning point in the development of Leeds city centre, with more to come after several years of little to no new activity.”
Two phases of Wellington Place have already been completed and the scheme has already become a blue-chip address with occupiers including insurance giant Allianz, consultancies Tower Watson and PricewaterhouseCoopers, and BSkyB
Planning permission was granted for 10 Wellington Place in September 2010.
That permission includes a further 106,000 sq ft of office space at number 3 Wellington Place, 155,000 sq ft at 4 Wellington Place and a further 59,000 sq ft at 5 Wellington Place.
Law firm Shulmans is the first to announce it will be moving into the new office development, when it relocates from its current base at 120 Wellington Street.
Mr de Blaby added: “Starting work on 10 Wellington Place is an exciting moment for us, and for Leeds city centre, but is only the first step towards developing the rest of the Wellington Place estate.
“We are already in talks with several potential occupiers for some of the other developments and look forward to being able to continue to build our business community.”