The 21-year-old has joined the Ibrox club on an initial 18-month loan subject to receiving a work permit and international clearance with an option-to-buy also inserted into the deal.
Last year, Sands helped New York defeat Portland Timbers to lift the MLS Cup for the first time in their history and was named the club's young player of the season.
He has been capped seven times by USA and played in their recent CONCACAF Golf Cup success, including the 1-0 final victory over Mexico.
A versatile player who can slot into midfield and in defence, Sands bolsters van Bronckhorst’s squad following the departure of Nathan Patterson to Everton earlier this week.
“James is a player who I have been aware of for some time," the Rangers manager said. "His versatility was a big attraction and I’ve been impressed with his attitude and mentality in the games that I have watched recently.
"He is a talented young player with areas of his game which we will endeavour to develop through our coaching.
“I am looking forward to getting him onto the pitch and starting to work with him.”
Sporting Director, Ross Wilson, added: “Signing James is a really interesting opportunity for us, and one we are all excited about.
"We reached agreement a couple of weeks ago for the transfer to be structured as a loan for this season and next, whilst we have negotiated and secured an exclusive option to buy beyond the initial loan period.
“Our scouting team has tracked his strong evolution over the course of the season with the MLS Champions New York City and we have identified a lot of potential in James. Gio has looked closely at what he can bring to Rangers and I know working with the manager and our staff, James will develop his game further here.
“Aside from his qualities with the ball, his versatility and tactical understanding, we also know that James is a brilliant character, positive personality and despite his young age, is already showing impressive leadership qualities.
"Naturally we faced competition from some excellent European clubs to sign James. I am delighted that he shares our belief that Rangers is the next step in his exciting journey.
“Finally, I extend my thanks to David Lee at New York City FC for his assistance in making this deal happen.”
Speaking as he arrived in Glasgow, young New Yorker Sands said: “I’m very excited to be joining Rangers Football Club.
"It is an incredible opportunity for me to join a club with such a winning history and worldwide fan base.
“Additionally, I’m looking forward to joining an ambitious and talented group of players and coaches. I am certain that Rangers will progress me as both a player and as a person.
“I would also like to thank NYCFC for the role they have played in my development so far. I have and continue to receive amazing support from everyone involved with the club.”