The agency is tasked with aiding Crossrail's consultation process as it seeks to develop the routes.
This will include gathering the views of councillors and officials, particularly planning officers, businesses and national politicians.
The AS Biss team, headed by senior consultant Lynette Huntley and overseen by chairman Adele Biss, has been recruited for an unspecified period of time and reports to Crossrail head of public affairs Bernard Gambrill.
Crossrail has been handed £154m by the Government to carry out a feasibility study and to develop the two routes, which run from east to west and north-east to south-west, and take preparatory steps towards building the tracks.
Some details of the routes were released earlier this year and, following lobbying from London mayor Ken Livingstone, Crossrail 1 will stretch to Heathrow Airport.
Crossrail is seeking to secure special powers to develop the routes through a hybrid bill - a government bill that contains clauses that affect specific individuals or companies - in parliament.