The communications company Teleperformance jobs will be based at their call centres in Glasgow, Erskine, Kilmarnock and Airdrie.
The jobs announcement will see its Scottish workforce expand to about 4000.
A total of 621 jobs will be full-time positions based in Blythswood Street in Glasgow City Centre. The remaining jobs will be a mixture of full-time and part-time posts across other sites in the West of Scotland.
The recruitment process is said to be already under way and will be ongoing for a number of weeks.
Posts will include customer service advisers, trainers and team managers.
Paris-based group Teleperformance generated more than £2bn in revenue last year.
Teleperformance carries out work for a variety of clients, including retail, technology and utility sectors.
First Minister Alex Salmond said: "This is a welcome boost and strengthens Scotland's position in out-performing the UK for securing inward investment."