At a meeting of the full council today, the Chief Executive of the authority Mike Greene said a number of councillors had contacted him asking what can be done to support the country.
Mr Greene said: "A number of members have contacted me over the past 24 hours in relation to the horrific events that are unfolding in Ukraine and if there is anything we as a council can do to show our solidarity with the people of Ukraine.
"I've consulted with group leaders and today I've instructed officers to put systems in place to light Scarborough town hall in the colours of the Ukrainian flag."
It is hoped that the blue and yellow lights, the colours of the flag, will be in place by the weekend, he added.
Russia invaded Ukraine in the early hours of Thursday morning and began bombing military targets near large cities.
Airstrikes have continued overnight into the early hours of this morning with attacks reported across the country - including the capital Kyiv.
Russian President Vladimir Putin sees Ukraine as historically part of Russia, and in 2014 Russian forces invaded and annexed Crimea in the south of Ukraine.