Following the success of the event in its first four years, in particular last year, Cllr Bill Chatt proposed to move forward with the decision, which was passed unanimously by the cabinet.
Cllr Chatt said: "This is one of those things that brings such a wealth of people seeing our coast in a tremendous way.
"When you watch it on TV you see the amount of people on the route and when it gets to the end, it comes around the castle headland and it's showing Scarborough in that light.
"But the most spectacular thing for me this year was the Filey situation. To be honest, I don't think you could get a cigarette paper between most of the people spectating out there.
"The amount of good publicity brought by this was absolutely phenomenal.
A vote of the full council will be required before any binding commitment to host a stage start or finish can be made.
If the council does bid and the town is chosen, it'll be the fifth consecutive year that a stage of the race has come to Scarborough.
It will cost the council Â£150,000, which will be paid from a projected surplus in its accounts, a report from the council’s tourism manager, Janet Deacon, stated.
However, if no surplus is achieved then the money would come out of the council’s general fund.
In her report, she added: “The proposed dates for the 2019 edition of the Tour de Yorkshire are 2nd to 5th May.
“The men’s race will take place over the full four days with the women’s race taking place on 2nd and 3rd. Welcome to Yorkshire are estimating in excess of 2.6m roadside spectators for the 2019 edition.
“For the fourth year, a mass participation sportive will also take place. More information in relation to the full detailed routes will be announced in October 2018.
“This will include where the start and finish towns will be, with the full route set to be unveiled in December. The council will be requesting that the route includes as much of the borough including the three main towns, Scarborough, Whitby and Filey, as possible.”