The ex-Whitehawk and Eastbourne Borough playmaker, who has played two of Rebels’ pre-season games, turned down better offers to sign for the club.
Since Worthing boss Chris White made it clear he wanted Budd last week, the experienced midfielder had calls from four other clubs.
White believes the signing shows their intent this season, and said: “I am very pleased. He has played at a higher level and since word got out last week he was available, he had a number of phone calls on Friday – some with a lot better than we were offering.
“He has played twice and trained twice with us and loved every minute of it, and is looking forward to getting back into his football again.”
On Tuesday night, Rebels suffered a disappointing 2-1 reverse at County League side Ringmer.
Despite the defeat, there were a number of positives as Steve Davies netted on his return from holiday and Tom Manton played an hour, while Luke Gedling also had a 20-minute run-out.
White said: “The result isn’t too important, but it was disappointing as we didn’t move the ball well and looked a bit lethargic.”
On Saturday, Rebels had put in a good performance, despite going down 2-0 to a full-strength Blue Square South side Eastleigh at home.
Worthing matched their opponents for long periods, although chances were at a minimum. Eastleigh struck twice in the second half, the first from Jordace Holder-Spouner on 50 minutes, before Danny Smith doubled the advantage.
White said: “We did okay. In the first half we tried to play a certain way and it was important we stuck to it, and we did.”