Solbakken played under Hodgson and was his captain when in charge of FC Copenhagen more than a decade ago.
Now the 44-year-old former Norwegian international has been appointed as new Wolves manager in succession to Mick McCarthy.
Hodgson told the Wolverhampton Express and Star: "I'm delighted because Stale is a good friend but also because I think it is an excellent appointment.
"I think it is a good, exciting move by Wolves. It's not an appointment many would have expected from a part of Europe from which English clubs do not usually recruit.
"But I can tell Wolves fans they have hired a superb coach. Stale is a bright, young and impressive coach with good ideas and I am confident he will do well."
Hodgson was also Copenhagen manager when Solbakken suffered a cardiac arrest in 2001 on the training ground which ended his career.
He said: "When something like that happens, it naturally brings you closer together and since then Stale and I have been good friends.
"But he was terrific captain for me, a fine footballer, and my assistant in that season at Copenhagen.
"I left after that and Stale took over and went on to have the most amazing success. Five championships in six years - that was a wonderful effort.
"He is a fine coach in my view with good ideas. I congratulate Wolves on an impressive appointment."