Mr Jackson, who lost his Peterborough seat at the general election, will join Mr Davis' team at the Department for Exiting the European Union.
The politician said he was "honoured" to have been offered the influential role at such a "historic juncture".
The Brexit campaigner represented the city in Parliament for 12 years but never served in government.
After losing his seat, he blamed his defeat on the Conservative manifesto, describing it as "electoral poison" and "shockingly bad".
Mr Jackson is not the first defeated Conservative to find a way back into the heart of politics since the election.
Gavin Barwell, who lost his Croydon Central seat, is now Theresa May's chief of staff while former Treasury minister Jane Ellison is working for Chancellor Philip Hammond.