All the 109 employee shareholders in WhitbyBird have voted in favour of the move, which will see ownership of the practice rolled into the foundation that has run Rambøll since 1970.
Rambøll's strengths include big bridges, energy and waste recycling.
'[The merger] gives us access to world experts on green energy,' said Whitby, who is confident that he will be able to bring increased expertise in areas such as wind energy and energy from waste to UK projects.
He also thinks that the Rambøll connection will help the practice be a serious contender for major projects such as the next Forth crossing.
Rambøll was the engineer for the Great Belt Bridge in Denmark, and also for the Oresund crossing between Denmark and Sweden.
Mike Crane, managing director of WhitbyBird, said he also believes that the overseas presence will bring benefits to the UK market, with Rambøll having a total of about 120 offices worldwide.
Crane said: 'More and more UK architects are asking us to go abroad and open offices with them. We can't afford to do this every time.'
Crane said he is now confident that delivery of projects can take place through the Rambøll offices.
Flemming Bligaard Pedersen, group chief executive officer of Rambøll, said, 'We can learn from the way that WhitbyBird traditionally works with architects - learn to understand the artistic side of what they are doing.'