Da Costa joined Cicero in January and had previously worked as the senior legislative aide to Theresa May’s office until November, a role she has held since the 2017 general election.
She is the first of many new aides Johnson will hire over the coming weeks and months.
Other names that are rumoured for roles in Johnson’s team include Rob Oxley as press secretary and Lee Cain as comms director, as well as another press adviser, James Starkie.
In his policy unit, a veteran of Johson’s London of Mayor team Munira Mirza is predicted to return to a policy role under the new PM.
Nick Hargrave, a former Downing Street special adviser under David Cameron and Theresa May, told PRWeek that Johnson will need to assemble his team quickly.
"Team Johnson do not have the luxury of time to feel their way through the obstacles. The operation will have to work properly straight away. Those first few days and weeks in Downing Street will be critical," the Portland director said.
"Civil servants in the building will be looking for steers on every call under the sun. But as his political team, your immediate responsibility is to find a way through the Brexit paralysis."
Hargrave believes that Team Johnson’s first task is to privately work out what sort of Brexit outcome they would prefer, and the mechanism for leaving.
He said another important role that may quickly need to be filled due to the possibility of a general election is campaign director at Conservative Campaign HQ, who is closely integrated with Number 10.