The transfer marks a milestone in Norwegian football as it is one of the largest player sales ever from a Norwegian club.
Only Sverre Nypan's transfer from Rosenborg to Manchester City and Albert Gronbaek's transfer from Bodo/Glimt to Stade Rennais were more expensive (£12.8 million); Celtic recently signed Kasper Hoegh for a similar fee.
For Viking, it is a historic transfer - and the result of a journey that began at the club’s youth academy when Edvin was five or six years old.
"It is, of course, a major deal for Viking, and we are proud that the club is capable of developing players who attract interest at this level," Sporting Director Erik Nevland said to the Viking website.
"But the most important thing for us is the story behind it. Edvin has been here since he was a young boy.
"Countless coaches and people within the club have been part of his journey, and this demonstrates what is possible for young players growing up at Viking."
The 21-year-old scored six goals and made seven assists to help Viking win the Eliteserien title for the first time in 34 years.
He also scored one of the all-important goals against Dinamo Zagreb last week to help his team secure a spot in the UEFA Champions League. In addition, he was also named Young Player of the Year in the domestic Norwegian league.
"Obviously, the ambitions of West ham are big, and it's also for me as a player," Austbo told West Ham's website.
"The talks I had with Nuno (Espirito Santo, head coach) and Nils Koppen (director of player recruitment) were amazing, and I just felt from the start that this was a good match and that I really wanted to come here."
Austbo is West Ham's seventh signing of the current transfer window, following midfielder Keiber Lamadrid, experienced defender Joel Veltman, winger Manor Solomon, midfielder Arne Engels, striker Joel Piroe and England U19 international Divine Mukasa.