Hours before the mid-season deadline closed, Da Silva formally had a three-and-a-half year deal with the Eels registered.
The move will allow him to begin training with the Eels immediately and line up for them in a fortnight against Penrith.
Da Silva was considered a leading part of the next generation of talent the Tigers were building themselves around, alongside Lachlan Galvin.
But he has now followed his close childhood friend out the door, after being stuck behind Apisai Koroisau at dummy-half.
"It's a bit disappointing for the club and us as a playing group," co-captain Luai said.
"We see the potential he has and the biggest thing for him was more opportunity.
"It's understandable for a guy that is behind Api. It's a tricky one. Everyone is entitled to that opinion, what they want and what they are chasing.
"All the best to him. I think he will get more opportunity at Parramatta anyway. He's going to be a very good player for a very long time."
Da Silva's move to Parramatta gives the Eels a genuine talent at No.9, after they have struggled to find a top-tier replacement for Reed Mahoney since his exit after 2022.
Koroisau is off contract at the end of next year, but the Tigers have decided to prioritise keeping the 32-year-old over Da Silva.
"I still think Api has a lot more years left in his legs," Luai said.
"I don't think he thinks that, but he does. And he's a big part of our team."
Elsewhere, the Sydney Roosters have brought Junior Tupou down from the Dolphins on a two-and-a-half-year deal starting this week.
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