A Police Scotland spokeswoman confirmed late Saturday that the two men, aged 61 and 45, have been arrested and remain in police custody pending a scheduled court appearance on Tuesday for alleged offences under the Railways and Transport Safety Act 2003, the BBC reported on Sunday.
The legislation covers carrying out pilot duties while under the influence of alcohol or drugs.
Police Scotland said that officers were called to the airport at 7.35 a.m., on Saturday. The pilots were the arrested before boarding flight UA162 which was expected to take off for Newark at around 9 a.m., but was cancelled.
Following the arrests, United Airlines said in a statement the safety of its customers and crew was "always our top priority", the BBC reported.
"We hold all of our employees to the highest standards and have a strict, no tolerance policy for alcohol. 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."
In a similar incident in 2017, two United Airline pilots were jailed for breaching drink-fly limits at Glasgow Airport.
One was sentenced to 10 months in prison, while the other was jailed for 15 months.
( With inputs from IANS )