The 24-year old arrived at Tannadice as a free agent, after securing his release from Dutch second division side Almere City FC.
Sneijder, brother of Galatasaray midfielder Wesley, is a product of the Ajax youth system - with spells at FC Utrecht and RKC Waalwijk prior to joining Almere in 2014.
As a highly-rated junior, Sneijder had been linked with a move to Real Madrid to follow in the footsteps of his older brother.
United manager Jackie Mcnamara, said: ““He has a fabulous pedigree and you can see his talent. He will become a fans’ favourite at Tannadice and this signing is a real coup for the Club.”
Rodney, who played for the Tangerines as a trialist in their pre-season games in the Netherlands, said: “This is the right time for me to explore Scottish football and I look forward to meeting my new teammates and the Dundee United fans. I want to help the Club achieve success this season.”
The Dutchman will be unveiled to the fans ahead of the final pre season friendly at home to Watford, today, Saturday 25 July, before kick-off.