The groups said industry input into the negotiations was crucial if businesses were to keep hiring and investing to boost the economy and raise living standards.
Carolyn Fairbairn, director general of the CBI, Adam Marshall, her counterpart at the BCC, and Simon Walker, the outgoing IoD chief who is joining the Department for International Trade as a board member, called for an "open and honest dialogue".
The letter is also signed by FSB chairman Mike Cherry, and Terry Scuoler, the EEF's chief executive.
Philip Hammond, the Chancellor, and Mark Carney, Governor of the Bank of England, have called for a transitional deal to smooth the UK's departure from the EU.
The letter says 2016 saw "unprecedented change for politics, society and business.
The Government must enter negotiations with the evidence needed to understand the implications of the decisions and trade-offs that lie ahead.
The decisions made in the year ahead will shape the prospects of people, businesses and communities across Britain for generations to come.
"The Government must enter negotiations with the evidence needed to understand the implications of the decisions and trade-offs that lie ahead.
"This evidence must be drawn from the experience of enterprises of all sizes."
The positive message departs from economic warnings published before the Brexit vote, which put forward the economic case for staying in the EU.
Official growth figures at the end of last year showed that the UK economy grew faster than previously thought in the three months immediately after the Brexit vote.
A recent CBI survey showed "almost every part" of the UK's private sector expects to take on more staff this year.
Key Brexit dates:
• January 2017: Supreme Court expected to deliver its ruling on whether Theresa May has the power to trigger Article 50 using a royal prerogative, rather than by an Act of Parliament
• March 31, 2017: Deadline Theresa May has set for invoking Article 50 by notifying the European Council of Britain's intention to leave the EU
September 30, 2018: Date by which EU's chief Brexit negotiator, Michel Barnier, wants to wrap up terms of Britain's exit from the Union
March 31, 2019: Date by which Theresa May wants to wrap up negotiations over Brexit
May 2019? Britain formally exits the EU, following ratification of Brexit by all other member states