The 53-year-old - a former Norway midfielder who has previously managed the national women's and U-21 teams - has signed a four-year contract, with the option to cancel if Norway do not qualify for the UEFA EURO 2016 finals.
He replaces Egil Olsen, who agreed to step down after a 2-0 loss at home to Switzerland in the latest round of FIFA World Cup™ qualifiers earlier this month.
The initial plan had been for Hogmo to pick up the reins on 1 January 2014, but it has now been decided he will oversee the final two Group E qualifiers - against Slovenia and Iceland - next month.
"I am very motivated to take on the job as coach," Hogmo, who will continue in his role with Swedish club Djurgarden for the rest of the season, said on the NFF's website.
"This is a job I have longed for my entire career. I am an innovative person, and want to put my stamp on how Norway will play.
"I initially said yes to take over from Egil from the new year. But when the NFF wanted me to take over for the remaining matches in the autumn - and he (Olsen) supported me - I was in no doubt. I'm hoping for a boost against Slovenia and Iceland."
Olsen, who appeared at a press conference in Oslo on Friday alongside Hogmo and NFF president Yngve Hallen, said: "I am glad that it is Per-Mathias taking over - it is a good choice.
"I was surprised when it was put forward that he would take over immediately, but I support it. I have also told Per-Mathias directly.
"In all probability, I would have been done anyway as coach in two or three weeks, so I do not see any great drama in this."
Norway head into the final two qualifiers fourth in the pool and with only a remote chance of securing a play-off berth to make the 2014 World Cup in Brazil.
Hallen paid tribute to the outgoing Olsen, however, and also expressed confidence in the new man.
"Egil has meant a lot," he said. "He has led Norway to two World Cup finals, and we defeated the biggest football nations. He was a groundbreaking coach.
"Hogmo is the right man to coach because he is technically and tactically strong, has good results, international experience and is constantly looking for new knowledge."