The phone-in show will be broadcast live every weekday from 4pm-7pm and is scheduled to begin in November.
Current drive-time hosts, James Hartigan and Petrie Hosken, will be moving to a different slot that has yet to be confirmed.
The controversial Whale is usually known as a late-night presenter and has been dubbed "the Voice of Reason".
Earlier this year, he was axed by UTV's TalkSport after breaching broadcasting regulations by urging listeners to vote for Boris Johnson in the London mayoral election. His remarks sparked several complaints to Ofcom following the show on March 20. He had been with the station since it launched as Talk Radio in 1995.
In August, Whale returned to work and guest-hosted a late-night LBC programme for a week. He then took over a more prominent slot in the schedule. Nick Ferrari continues to host the LBC 97.3 breakfast show.
The Times has just signed a six-month deal to sponsor the breakfast slot. The package consists of sponsorship and presenter-read ads, using newspaper editorial content from The Times that will change daily.
LBC 97.3 is owned by Global Radio, which is in the initial stages of integrating its business with GCap Media, the company it purchased in March 2008 for £365m.
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