"We admit that Egil perceived the situation as him being fired, even if that wasn't our intention," NFF president Yngve Hallen is quoted as saying.
"The NFF has learned from this incident and it will facilitate better handling of similar cases in the future."
A run of poor results in World Cup qualifiers led to a board meeting on September 26, and Olsen has said he felt he had no choice but to resign. He was quickly replaced by Per-Mathias Hogmo.
"Both parties have agreed to put this behind them and to wish the national team and Per-Mathias Hogmo the best of luck," the NFF said.
"Egil Olsen is also satisfied that the issue has been resolved."
Norway finished fourth in their World Cup qualifying group and will not be at next year's tournament in Brazil.
(Reporting by Philip O'Connor in Stockholm; Editing by Alison Wildey)
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