Under the terms of the 30-year agreement, the Barbican could host more than 350 events and 50 conferences a year, bringing between £9m and £11m to the York economy annually.
The £2m investment will include a refurbishment of existing facilities which will include a dedicated restaurant, meeting rooms and improved public and back-of-house spaces.
York & Scarborough Conferences business tourism marketing manager Laura Freer said: "We are delighted to add the centre to our portfolio of events venues and the addition will pay dividends long term to the local economy. This venue is something very special which will make any event stand out from the crowd."
SMG is working with partners Arup and Fuse Design on the redevelopment, and construction work will start on site in early January 2011.
Once completed the Barbican will employ more than 60 staff and have a capacity to host 1,500.
SMG Europe theatres director Nick Reed said: "SMG is delighted to have been awarded the contract to operate the York Barbican and we are full speed ahead to get the Centre open for next May. We are looking forward to a long and successful association with the city."