The £9.9m state-of-the-state office opened its doors last year and has become a community hub for the area, with residents being able to access a variety of local services in one location.
In the new facility, housing and social work staff are working alongside a Registrar's Office, a Marriage Suite and conference facility.
Further partner agencies are expected to relocate into the building soon.
The new library is more than double the size of its old Ayr Road facility and incorporates a learning suite for lifelong learning classes as well as computers with internet access. There are also various meeting rooms which are available for community groups to hire.
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Mr Mackay said: "It was a delight to be at the opening to see first-hand East Ayrshire Council regeneration work and the commitment of staff to re-establish Cumnock town centre. With the movement of a number of council buildings to this one location there is a real sense of community.
"The hard work and financial investment of this project is real testament to local planning, regeneration and dedication to help contribute to the local community and the economy."
While East Ayrshire Council Leader, Councillor Douglas Reid, added that the project had "breathed new life into the town", increasing footfall and trade in the town centre.
Rothesay House is just one of a series of regeneration projects in Cumnock and part of a £17m masterplan of restoration and renewal for the town centre.
To date, £1.5m of Conservation Area Regeneration Scheme grants have been approved to owners of historic buildings in the area, including £850k to Cumnock Town Hall and a £650k refurbishment of the Baird Institute.
(JP)
