Arena was awarded the business after a final shoot-out with the incumbent.
Eurostar has informed all agencies involved in the process that "following a standstill period", Arena Media will enter into a contract with the high-speed passenger train service on 21 June.
As part of Eurostar's feedback, agencies have received scores from the client, rating their performance in comparison to Arena Media.
Walker, UM, Rocket and Maxus were all previously involved with the process, before Eurostar whittled it down to Vizeum and Arena Media.
Eurostar launched a tender for its media arrangements last October, as part of a statutory review. Vizeum had held the account for more than six years.
Eurostar spent a total of £6.5m on media in the year to the end of March, according to Nielsen.
Emma Harris, the director of sales and marketing at Eurostar, said: "Following a rigorous OJEU pitch process, Arena have been selected as the winning agency. We are in a 10-day stand still period with contracts being signed next week.
"The pitch was highly contested and the quality of submissions was incredibly high. We will continue to work with our incumbent agency Vizeum until the end of September and would like to thank them for their excellent hard work and dedication they have given us during five successful years working together."