John passed a medical and trained with his new teammates under the watchful eye of HSV coach Bert van Maarwijk, who called the 21-year-old up to the Netherlands squad when he was in charge of the national side.
"I know Ola well and I am convinced he will soon make a big contribution," said van Maarwijk of the player who was born in Liberia but moved to the Netherlands as a child and made his name with FC Twente before joining Benfica in 2012 for €9m.
His arrival is set to be followed by that of another Dutchman, with Hamburg on the verge of completing the signing of Ouasim Bouy, also on loan, from Juventus. Midfielder Bouy, 20, spent last season on loan at Brescia and will join Hamburg pending a medical.
HSV, who are 14th in the table halfway through the season, are due to host Schalke on January 26 in their first match of 2014.