Ambani spent 2.42 billion rupees (US$59 million; €49 million) on an Airbus-319 corporate jet fitted with a plush bar with mood lighting, a master bedroom, showers and a state-of-the-art entertainment cabin.
The jet rolled into Mumbai's airport in time for his wife Nita's 44th birthday on Thursday, the Mumbai Mirror newspaper reported, citing unidentified individuals.
Ambani is the chairman of Reliance Industries, a diversified Indian business conglomerate. His wife runs a top school in suburban Mumbai and heads a host of charitable trusts.
A Reliance company spokesman said he was not authorized to confirm the news report.
According to the paper the jet has a separate cabin for business - fully equipped with wireless and satellite communications systems - and another entertainment cabin with games, music and movies.
Reliance Industries is largely focused on petroleum and petrochemicals.