The technology business, which has plans to become the city’s first unicorn business, recently raised £2m from global investors.
It has since quadrupled in size, with the number of employees increasing from 10 to over 50 in the last eight weeks.
Launched in 2014 by international students Chitresh Sharma and Louis Schena, who studied at the University of Strathclyde, the loyalty scheme was initially used by independent businesses to build customer relationships and improve retention.
Consumers who join the loyalty scheme can access a diverse range of awards unique to each merchant.
Swipii has enlisted KPMG to provide business advice and manage its growth as it rolls out in cities across the UK.
Since Swipii was founded, it has signed up more than 1,000 merchants.
Recent growth projections suggest that the scheme will have over 5,000 merchants by March 2017.
Newcastle University is set to adopt the loyalty scheme across its canteens and Swipii recently concluded a deal with Glasgow’s secondary schools that will enable pupils to collect points for choosing healthy lunch options.
A London sales team was recently appointed to grow customers in the capital and in the next six months the scheme will be introduced to small and medium sized businesses (SMEs) to other English cities including Manchester, Liverpool and Leeds. Plans are also in place to target overseas markets such as Spain and France.
Phil Charles, KPMG’s head of enterprise in Scotland, said: "KPMG is delighted to be working with Swipii, one of Scotland’s most exciting emergent technology businesses.
"Our investment in the Enterprise team was specifically to help fast growing entrepreneurial businesses just like Swipii to realise their expansion plans.
"We look forward to working with Louis and Chitresh to help them achieve their growth as Swipii targets new markets both in the UK and overseas.
"It is also rewarding to know that our support could contribute to Swipii creating new high quality jobs and boosting the economy, particularly in Glasgow where the business is based."
Louis Schena, co-founder of Swipii, added: "KPMG is a strong, global brand with a diverse range of services and expertise. We liked the retail sector experience they could bring to the table and we were impressed by the Enterprise team’s experience in supporting entrepreneurial, growing businesses.
"We’ve got big plans for Swipii in the coming months and years. KPMG’s ‘can do’ attitude is exactly what we need to achieve our ambitions."