The 29-year-old, whose finest moment came in the 2014 World Cup quarter-final penalty shootout when he was sent on as a substitute and saved two Costa Rican spot-kicks, has signed a one-year permanent deal with Brighton.
He had joined the Seagulls on loan at the beginning of the season.
Krul, capped eight times, brings to a close 12 years at Newcastle, for whom he made 184 appearances in all competitions.
Krul, who has also played for Dutch giants Ajax, made his debut in Tuesday’s League Cup defeat by Bournemouth.
“Everyone at Newcastle United would like to thank Tim for his long service to the club and wish him and his family well,” read a statement from Newcastle.
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