Gomes, 21, joined Leeds from Liverpool last summer, where he has previously worked with Beale. But his time at Elland Road was a disappointing one, making only two senior appearances in the Carabao Cup.
Beale joined Liverpool's academy back in 2012, and left the position of Under-23 coach in December 2016 to join Brazilian side Sao Paulo. Now, he is a coach under Steven Gerrard at Rangers.
Beale wished Gomes luck on Twitter, and stated that it was pleasing to see him move to a new club where he would become settled. He has signed a two-year deal with the second-tier club.
Good luck to Madger Gomes. Nice to see him settled at a new club. https://t.co/AzSG581Eh9— Michael Beale (@MichaelBeale) June 11, 2018
Gomes is the first of what is expected to be somewhat of a summer exodus at Elland Road this summer, with plenty of Victor Orta's signings failing to meet the required standard.
The young midfielder failed to make the grade in Yorkshire, with the likes of Kalvin Phillips, Ronaldo Vieira, Adam Forshaw and Eunan O'Kane above him in the pecking order. He was only one year into a three-year deal.
A three-time Spain Under-18 international, Gomes joins a side that finished in tenth place in France's second division last season and he will be hoping to help Sochaux mount a promotion challenge this time around.