"These pilots were immediately removed from service and we are fully cooperating with local authorities.
"At this time, we are working to get our customers back on their journey as soon as possible."
According to Police Scotland the men remain in custody with an initial court appearance scheduled for Tuesday 6 August, where both men will be tried for offences under the UK Railways and Transport Safety Act.
The UK legislation sets the breath alcohol limit for active pilots is equivalent to the New Zealand drink drive legal alcohol limits. (25 microgrammes of alcohol in 100 millilitres of breath exhaled.)
In 2017 two previous United pilots were jailed for being in breach of drink-fly limits at Glasgow Airport.
Pilot Paul Grebenc, 35, received 10 months in prison with his co-pilot Carlos Roberto Licona, 45, receiving 15 months.
Last October, a pilot for Japan Airlines was arrested at London Heathrow after proving to be 10 times over the alcohol limit. Katsutoshi Jitsukawa was preparing to fly a Boeing 777 and its 244 passengers to Tokyo, when he was arrested for the offence.