The 24-year-old was a free agent after securing his release from Eerste Divisie club Almere City.
Sneijder had a successful youth career at Ajax before starring for FC Utrecht and RKC Waalwijk prior to joining Almere in 2014, and he is the brother of Galatasaray midfielder Wesley.
The Dutchman will be unveiled to the United fans ahead of the friendly against Watford at Tannadice today.
United boss Jackie McNamara said: “I am very happy to sign Rodney. He showed great desire and application whilst training with us during pre-season and he will add great quality to our midfield.
“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.
“I look forward to working with Rodney and seeing him in our team this coming campaign.”
Sneijder, who played for the Tangerines as a trialist in two of their three pre-season games in the Netherlands, is looking forward to meeting his team mates ahead of his first training session on Monday.
“I enjoyed my time with the squad over in the Netherlands and I know from speaking to the Manager where he believes this team can go. This is an excellent opportunity for me to develop and progress as a player,” he said.
“This is the right time for me to explore Scottish football and I look forward to meeting my new team mates and the Dundee United fans. I want to help the club achieve success this season.”