The Lotto Soudal team set up the German national champion perfect, leading Greipel safely through the final corner at the head of the peloton, with Jens Debusschere providing the perfect lead-out at the end of the 161km stage from Glasgow.
"It is really nice to start off this tour with a victory. We have reached our goal already from the first day. Everything else is a bonus”, Greipel said.
Greipel avoided a final crash further back in the peloton on the final corner, removing the likes of Mark Cavendish (Dimension Data), Elia Viviani (Sky) and Dylan Groenewegen (LottoNL–Jumbo) from contention.
The stage win and time bonus gives Greipel a single second lead over Jasper Bovenhuis (An Post Chain Reaction), who picked up the time bonuses at all three of the day's intermediate sprints from a breakaway to sit second overall, with Ewan (Orica-BikeExchange) third.
Bovenhuis took the sprint jersey from a five-rider breakaway that formed early on while the race lapped Glasgow in front of packed crowds throughout the city centre.
Alongside teammate Emiel Wastyn, ONE Pro Cycling's Peter Williams, NFTO's Johnny McEvoy and JLT Condor's Tom Moses the quintet spent the majority of the stage out front, but a watchful peloton never let them gain more than four minutes.