The team said Boullier would report to a yet-to-be-appointed McLaren Racing Chief Executive Officer, who would in turn answer to group chairman, shareholder and former principal Dennis.
Jonathan Neale will fill the chief executive officer role temporarily. There was no mention in the statement of Martin Whitmarsh, who was team principal last season but has been ousted by Dennis.
"I regard this appointment as an honour, a privilege and a wonderful opportunity," said Boullier, who has been replaced at troubled Lotus by co-chairman Gerard Lopez, in the statement.
The Frenchman, who managed to keep Lotus on an even keel last season despite mounting financial problems, said he was "hugely excited" at the prospect of working for the former champions.
"I'm both eager and determined to play an active part... within a new operational structure, to bring about the changes that will deliver success," he said.
"I want to take this opportunity to assure the McLaren Racing workforce that I'm utterly determined to match their famous passion and commitment to win."
McLaren had a miserable season last year, failing to secure a single top three finish in what was their worst performance as a team since 1980.
This season they have brought in Danish rookie Kevin Magnussen as partner to 2009 world champion Jenson Button, the most experienced driver in Formula One.
Dennis said Boullier's arrival was part of an ongoing restructuring of senior management at the team.
"I've already personally conveyed to the entire workforce of the McLaren Group, which includes McLaren Racing, the values, principles and mindset that I intend us all to adopt, going forward," he said.
"I'm firmly of the belief that, once McLaren Racing's restructured senior management team has been assembled, together we'll begin the march back to full competitiveness."
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