Sigurdarson is expected to pen a four-year contract at Molineux after an undisclosed fee was agreed with Lillestrom. The 21-year-old is committed to playing in the Norwegian Premier League outfit's next three games before arriving in Wolverhampton on July 13 to become boss Ståle Solbakken's first signing.
Solbakken said in a club statement: "I am very pleased that an agreement has been reached for us to sign Björn. He is an exciting young prospect who has the quality to help us achieve our aims both in the short and long term."
He added: "We look forward to the deal being completed next month after which Björn will be able to join us as we prepare for the new season."
Wolves CEO Jez Moxey said: "Negotiations have been slightly more complex than usual due to the Norwegian League being halfway through the season, but as a result of extensive discussions we now have an agreement.
Sigurdarson, the half-brother of former Wolves midfielder Joey Gudjonsson, has been in impressive form for Lillestrom this term, netting seven goals in 11 appearances.