The 27-year-old second-rower was in the final season of his Rhinos contract, but this week joined Tigers with immediate effect on a deal lasting until the end of 2024.
Mellor, a Challenge Cup winner with Rhinos in 2020, could make his debut in Sunday’s home game against Catalans Dragons.
His last appearance for Rhinos was the Easter Monday defeat at Castleford, when he was substituted because of a sternum injury.
He made his comeback two weeks ago on dual-registration with Bradford Bulls, but - after dropping down Leeds' squad number order in pre-season - had fallen behind fellow second-rowers James Bentley and Morgan Gannon.
He had been linked with Tigers for next term, but the immediate move came out of the blue.
Explaining the background, Mellor revealed: “I had signed at Cas for next year, that was all sorted.
“As far as I was concerned, my contract was signed, that was all done and I was focused on Leeds until the end of the year, but then Cas came knocking at the door, saying ‘do you want to come this year’?
“Radders [Tigers coach Lee Radford] messaged me and I spoke to [his agent] and I thought it was great to feel wanted. I felt this club wanted me for me.
“It was going to be a bit of a struggle for me at Leeds so I jumped at the opportunity of ‘I can go there and help this club and they can help me as much as I can help them’.
“That was great, it was a good balance and an opportunity I didn’t want to say no to.”
Mellor admitted: “I sort of pushed it a little bit and I had to have a couple of awkward conversations with Rohan [Smith, Rhinos’ coach] and with Gary [Hetherington, chief executive].
“They obviously knew I [was leaving] for next year, but [I had] to say to them ‘I want to leave now, this club wants me, I am ready to go’. “
Mellor was coached by Smith at his first professional club, Bradford Bulls, but didn’t get to play under him for Leeds.
“It was such a strange period,” he recalled.
“I was in the midst of signing at Cas when Rohan came in.
"My Cas contract needed signing and I said to Rohan ‘I know you’ve just landed, but I have got 24 hours where something needs sorting.
“Leeds couldn’t facilitate it, understandably they couldn’t make a decision, so I just took the onus on myself to sign a deal and be done with it and be happy coming to Cas.
“But in terms of not playing for him, it is a shame. I have a good relationship with him, he is a good fella and I’m sure he will go on to be successful for that club.”
Jack Broadbent, who will also leave Rhinos in the autumn - and is set to join Tigers next year - this week moved to Featherstone Rovers on loan until the end of this season.
But Mellor said it isn’t a case of clearing out players who are set to move on anyway.
“I don’t think Rohan’s like that,” he said. “He is quite straight with you.
“He wants the best for whoever’s playing for him now, at this time.
“There’s no ulterior motive with him - if you’ve signed elsewhere he’s not going to not play you.
“He’s going to be fair with everyone. I think it’s probably more of a coincidence that’s happened.”