Blackwell, 25, suffered a bleed on the brain in a loss to Eubank in March and was put in an induced coma.
The offer comes despite Blackwell saying Eubank and his father were "inhuman" in how they reacted to his life-threatening injuries post-fight.
"I ended the guy's career," Eubank Jr told ITV's Good Morning Britain.
"He said everything was OK and that there were no hard feelings, but I've stopped him being able to make a living.
"I wanted to come and see him because I had something for him, and that something is my British title belt."
READ MORE: 'I could see no light at the end of the tunnel' - Blackwell's trainer
Blackwell woke from his coma a week after the fight, which was stopped in the 10th round, without requiring an operation.
Speaking to the Sun on Monday, Blackwell was critical of the Eubanks' decision to hold a news conference while he was still in hospital.
"I was shocked when I first heard the things he had been saying because we had a little talk on social media," added Eubank Jr.
"I believe that the belt is a goodwill gesture - I'm still ready to come and give it to him.
"The guy's a true warrior, regardless of what's been said, the only thing that's important is that he is now OK, he's with his family and he can live a normal life with no restrictions."

Holdsworth, 47, beat takeover offers from banker Roger Tamraz and Bolton Wanderers Supporters' Trust.
The club, owned by Eddie Davies, are £172.9m in debt and have been trying to find a buyer for a number of months.
The Championship strugglers are scheduled in the High Court on Monday over a £3m unpaid tax bill.
It is hoped the takeover will soon be completed as Wanderers must let the High Court know by 19 February if they are going to enter administration, and also prove they have funds to continue trading.
Former Wimbledon and Brentford forward Holdsworth spent six seasons at Bolton, scoring 52 goals in 188 appearances.
BBC Radio Manchester also understands the sale of the Trotters' training ground at Euxton has yet to be finalised, with League One side Wigan making an approach.
British middleweight champion Chris Eubank Jr has offered to give his title belt to retired opponent Nick Blackwell as a "goodwill gesture".
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Bolton Wanderers have given preferred bidder status to former striker Dean Holdsworth's Sports Shield consortium, reports BBC Radio Manchester.