He started his career as a shopkeeper in Tromsø, but life behind the counter became monotonous. At 19, he spent the winter at Hopen in Svalbard (1908-09). He later went to the island of Jan Mayen and various fishing grounds in Svalbard. He also spent several winters in Greenland, first in Northeast Greenland (1928–30), at Southeast Greenland (1931–33) and at Northeast Greenland again (1939–42). During World War II, he belonged to a sled patrol under Danish command that patrolled the Greenland coastlines on the lookout for German soldiers (1942–45). 
In total, he went on 40 hunting trips to the Arctic regions, and wintered there for 25 of them. The animals that were usually hunted in these regions included Arctic fox, walrus and seal, but Rudi is best known for having killed a total of 713 polar bears. The winter of 1947 was his last time hunting in the Arctic.
Rudi spent his last days in the town of Tromsø. He was known for his cheerful personality and spent a lot of his retirement days in the Ølhallen pub in Tromsø, where he gladly spoke to everybody who would listen about his adventures in the Arctic. In 1953, he was awarded with the King's Medal of Merit (Kongens fortjenstmedalje). He has also been honored with his own permanent exhibition in the Polar Museum (Polarmuseet) at Tromsø alongside other Arctic explorers, including Roald Amundsen and Fridtjof Nansen. 
- "Henry Rudi". Store norske leksikon. Retrieved April 1, 2018.
- Marit Anne Hauan. "Henry Rudi". Norsk biografisk leksikon. Retrieved April 1, 2018.
- "Henry Rudi". polarhistorie.no. Retrieved April 1, 2018.
- "Kongens fortjenstmedalje". lokalhistoriewiki.no. Retrieved April 1, 2018.
- "The Polar Museum". University of Tromsø. Retrieved April 1, 2018.