"This could be the club where I finish my sporting career," 30-year-old midfielder Nekounam told the club website after signing his deal which has options for automatic extensions in the future.
Nekounam joined Osasuna in 2006 and has won over 100 caps for Iran.
Forward Masoud, 26, had surgery on his left foot on Tuesday after suffering an infection from an operation on the same problem back in April.
The Pamplona-based side finished a creditable ninth in La Liga.
