The Tigers put in a combined bid of £9m for the two players which successfully triggered the £3.5m release clause in Odubajo’s contract.
The 22-year-old completed his medical and has now signed a three-year contract, with the deal announced on both club’s websites on Friday.
But Brentford want more than the £5.5m on the table for forward Gray and have told Hull they will need to increase their bid if they also want to bring the former Luton frontman at the KC Stadium.
Odubajo joined Brentford for £1m from Leyton Orient and became a regular in Mark Warburton’s side last season as they secured fifth place in the Sky Bet Championship. He played 49 games for them, scoring three goals.
He also won six England Under-20 caps at the Toulon Tournament earlier this summer.
Gray made the move to Griffin Park on the same day as Odubajo – June 27, 2014 – after joining from then-Conference champions Luton for £500,000. He scored 18 goals in 50 appearances for Brentford.
On the Hull website, Odubajo said: “I’m pleased that everything is done now.
“Unfortunately it didn’t happen in time for me to play on Saturday, but I’m looking forward to playing for this club and I’m ready whenever the manager wants to select me.”
Brentford head coach Marinus Dijkhuizen said on his club’s website: “I would like to wish Moses all the best with his move. I enjoyed working with him and I can see what a talented player he is.
“He will be a big loss to us, especially at this stage of pre-season. We did not want to lose him, especially to a rival team in our division.
“However, this will give a chance to another player. We have a lot of quality players and enough quality in the squad that we are ready to face Ipswich tomorrow. We will now be looking to get a replacement in to build our squad back up.”
Phil Giles, Co-Director of Football at Brentford , added: “Moses had a great season last year. He was brought to the club because of his undoubted talent and he has developed over the last 12 months.
“On behalf of everyone at the club I would like to wish Moses all the best for the future and thank him for his efforts in a Brentford shirt.”