"Ajax and AS Roma have reached an agreement concerning the transfer of Maarten Stekelenburg," the Dutch club said on their website on Saturday.
"The agreement with the Italian club... depends on a number of conditions being met."
Stekelenburg, 29, has been at Ajax since 2002, winning the Dutch League and Cup three times each. He has played 40 times for the Netherlands and was in the team which reached last year's World Cup final. He replaces Brazilian Doni, who has been sold to Liverpool.
AS Roma, who finished sixth last season to qualify for the Europa League, appointed former Barcelona and Spain player Luis Enrique as coach last month and he has promised to get his team playing like the European champions.
They have since bought 20-year-old Bojan Krkic from Barcelona for 12 million euros in an unusual deal that includes a commitment by the Catalans to buy the Spain under-21 forward back in two years.
They have also signed 19-year-old attacking midfielder Erik Lamela, considered one of Argentina's brightest prospects, from River Plate and his more experienced compatriot, defender Gabriel Heinze, from Olympique Marseille.
Roma were taken over in April by a consortium led by United States businessman Thomas Di Benedetto, which bought a 60 percent stake in the club.
