The 35-year-old took temporary charge of the club in February after Michael Laudrup was sacked, and has now been appointed permanently after guiding the Swans to safety following a poor start under the axed Dane.
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"We are delighted to confirm Garry as our new first-team manager," he told the club's official website.
"As a Board of Directors ... we unanimously agreed that the timing was right for Garry to be offered the job on a permanent basis.
"Garry represents all the strong values we hold so dearly as a football club and everyone is looking forward to working with him.
"We have all been impressed with his work-rate and commitment since taking over the reins in February and how he adapted in very difficult circumstances to secure the points we needed to remain in the top flight.
"Garry will work with the current staff to refocus and improve the playing squad over the summer in order to build a strong, competitive team for another big challenge that lies ahead next season."
Monk's first game in the full-time role is Sunday's trip to Sunderland on the final day of the season.