The move was sealed late on transfer deadline day and checks were being made to ensure the relevant paperwork was submitted before the 6pm deadline.
Jacobsen, 30, has earned 35 caps for his country and played 16 times for Blackburn after joining them on a free transfer from Everton last summer.
Hammers boss Avram Grant, whose side have shipped nine goals in their opening three Premier League games, had made recruiting a new right-back a priority. Jacobsen began his career at Danish side Odense and and played for Hamburg, FC Copenhagen and Nuremberg before joining Everton two years ago.
His appearances for the Toffees were limited by a shoulder injury and he was allowed to leave after one season.
Jacobsen played in all three of Denmark's matches at this summer's World Cup, where they failed to progress from their group.