Veltman agreed a three-year contract with the Premier League side.
The 28-year-old helped Ajax win the Dutch title three times after coming through the club’s vaunted academy.
“We’re delighted to welcome Joel to the club,” Brighton boss Graham Potter said.
“He has terrific experience from his time with Ajax including the Champions League and, of course, with the Dutch national team.
“He’s an excellent defender who can play at right-back and at centre-half, but he’s also comfortable in possession.
“He is really looking forward to the challenge of playing in the Premier League and we’re delighted he is now a Brighton player and we’re looking forward to working with him.”
Capped 22 times by Holland, Veltman was part of the 2014 World Cup squad and also played in Ajax’s Europa League final defeat to Manchester United in 2017.
He becomes the second arrival at the AMEX Stadium this week after England midfielder Adam Lallana joined the Seagulls following his departure from Liverpool.