The 23-year-old forward scored 11 times for the Robins last season.
White came through the youth ranks at Millwall but despite being involved in the squad a number of times never made a first team appearance before eventually being let go by the Lions in 2019.
He first headed just a few miles south to Dulwich Hamlet, before heading to the War Memorial Stadium 18 months later.
Worthing boss Adam Hinshelwood has been a long term admirer of the talented wide man: “We were very close to bringing Lewis to the club last season and I’m delighted we have added him to our group. A really exciting player who I can’t wait to get to know and work with”