They will replace two of the thee tugs currently operated by Orkney Islands Council Marine Services.
Odin of Scapa will be the first to be delivered and is expected to arrive in Orkney around the end of May next year, with Thor of Scapa due later in the summer of 2020.
In the poll, people were asked to cast their vote for four groups, each containing three names.
In all, 566 votes were cast, with 315 of them for the group containing the names Odin, Thor and Vale. The name Vale of Scapa will be held in reserve and used if the Council decides in future to replace the third tug as well.
A winner has been drawn from the votes for the most popular group of names. Isobel Thompson from Westray has been invited to take part in the naming ceremony for Odin of Scapa and offered the opportunity of a family trip aboard the new tug.
Graham Sinclair, Chair of the Council’s Development and Infrastructure Committee, said: “As names that strongly reflect Orkney’s Norse heritage, these are an excellent choice for the new tugs.
“Tugs operated by first class crews play a vital role at the heart of our harbour operations and have helped support the welcome growth in maritime activity we’ve seen in local waters in recent years
“I am pleased we are investing in even more capable vessels, which will ensure the continuation of 40 years of support for the Flotta Terminal and, more recently, the significant growth in ship to ship work - and allow us to make the most of current and future marine business opportunities, greatly benefiting the economy of the islands.”
The design and build contract for the 32-metre tugs was secured by Sanmar Shipyards of Turkey after a competitive tendering exercise.
Construction is taking place at Sanmar’s new specialist tug building facility at Altinova, about an hour south of Istanbul, where work on both tugs is progressing well - as can be seen from the latest photographs taken during a recent inspection by Orkney Marine Services towage staff.