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Irish international Healy was stretchered off after hurting his ankle during the Lions' 69-17 victory over Western Force on Wednesday and is due to undergo a scan in Brisbane on Friday.
Corbisiero, 24, is currently in Argentina with the England squad, but the Lions said he was scheduled to fly out to Australia "as soon as possible".
"Cian has had an X-ray and, while his left ankle is not broken, he will be assessed further when we get to Brisbane," said Lions head coach Warren Gatland.
"In the meantime, we need to get Alex over here as soon as possible and I am thankful to (England head coach) Stuart Lancaster for letting him go so quickly."
Lancaster said he was happy for Corbisiero to leave.
"We are delighted for Alex," he said in a statement. "It's very pleasing for him after he missed the Six Nations through injury, and he goes with our full support and blessing.
"All the England players and management couldn't be more pleased for him to get this opportunity."
In a separate development, Healy is due to go before a disciplinary panel after being cited for allegedly biting Force scrum-half Brett Sheehan.
The Lions' next tour fixture is a game with Queensland Reds on Saturday.
