The 35-year-old has served as head coach at the Liberty Stadium since Michael Laudrup was relieved of his duties in February, but was only initially appointed on a temporary basis.
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"It is the proudest moment of my career," he told the club's official website. "I'm honoured the club thinks so highly of me to give me this chance. It's the opportunity of a lifetime and one I fully intend to take.
"I have had a taste of the job for the last three months and it's something I've really enjoyed. Now I'm really looking forward to the next phase in my life and the club's progression.
"I'll be looking to stamp my authority on the squad and the club and take it forward. I have a plan in my mind and with the help of the chairman and the board how to implement it.
"I have been given a massive responsibility to manage this proud football club, but I have always been a person that enjoys and relishes responsibility, so I am looking forward to the challenge.
"I have been at this football club for 10 years and I know what Swansea City means to everyone in the community and beyond. That's what will drive me on to produce a successful team that plays attractive and attacking football.
"I want everyone connected to this club to be proud of the team.
"I am under no illusion how much hard work is needed going forward, but I am willing to put that hard work in by giving everything I have to ensure Swansea City is a success."
Swansea, who are 13th, visit Sunderland in their final match of the current campaign on Sunday.