However, the court has yet to decide if the government acted legally when it changed the rules of the referendum, making it easier to oust the president.
PM Victor Ponta accuses Mr Basescu of exceeding his authority and of meddling in government affairs.
Conflict between the two has stalled political decision-making in Romania.
Judges deliberated for nine hours before deciding that last Friday's vote in parliament was legal. The referendum is scheduled for 29 July.
On Tuesday, the court will rule whether Mr Ponta's government acted legally when it changed the rules of the referendum.
The changes make it possible to oust the president with a simple majority of all votes cast - not of the whole nine million-strong electorate, as under the previous rules.
Mr Basescu insists he should not be impeached as he has not committed any "serious violations of the constitution".
Mr Ponta said he hoped that Romanians would vote against the president, heralding a new era.
Conflict between the president and prime minister comes as Romania finalises agreements on an IMF-backed economic aid package.
Mr Ponta's government has been sharply criticised by German Chancellor Angela Merkel for persistently breaking EU democratic norms since it came to power six weeks ago.
Mr Ponta, who heads the Social Liberal Union (USL), is himself under pressure to resign over allegations of plagiarism.
He denies that he plagiarised large sections of his doctoral thesis, which was published in 2003.
Romania's constitutional court has upheld a parliamentary vote suspending President Traian Basescu, allowing a referendum on his impeachment.