Assistant Chief Constable Bernard Higgins was speaking at a security briefing ahead of high-profile weekend events.
Officers remain on high alert during the General Election and Scotland-England Hampden Park World Cup qualifier following the terror attacks in London and Manchester.
Mr Higgins said: “Armed policing officers will be deployed at both Murrayfield and Hampden Park stadium but the public should not be alarmed by this and they should be reassured that we have put in place contingencies to deal with any eventuality.
“Police Scotland is prepared and has the capability to respond effectively to any incident but it is important that people carry on their business as normal.
“We will not let the threat of terrorism impact on our everyday lives. Enjoy the events over this weekend and be assured that Police Scotland have plans in place to keep people safe.”
The Evening News reported yesterday how organisers have advised gig goers not to bring big bags and only carry essentials amid tight security.
Checks will be stepped up when tens of thousands of fans flock to see the former Take That star perform.
Concert goers have been told to arrive early with a pre-show bar outside the stadium open from 3pm and the arena itself from 5pm.
Food and drink brought from outside will be confiscated while drinking water will be available at various points around the stadium.
Support act Erasure are due to start their set at 7.30pm with the Angels singer expected to take to the stage at around 8.45pm.
A Scottish Rugby spokesman said: “The safety of all visitors is of paramount importance. The safety measures we have in place are constantly under review, in liaison with the relevant agencies.