Prime Minister Yingluck Shinawatra now faces the difficult decision of whether to submit the bill for royal endorsement or wait until the Constitution Court rules on an opposition challenge.
The coalition MPs and senators remaining in the House after the Democrats' walkout approved the amendment by a vote of 358-2 with 30 abstentions
The opposition says the bill, which authorises the election of all 200 senators, makes major changes to the state's structure and is likely to affect the balance of power among the legislative, executive and judicial branches and independent organisations.
Before the voting began at 10am, opposition chief whip Jurin Laksanavisit of the Democrats proposed a debate on whether voting should be postponed since the Constitution Court had now accepted for consideration a challenge to the amendment.
But MPs of the governing Pheu Thai Party opposed any further debate, citing parliamentary meeting regulations.
House Speaker Somsak Kiatsuranont then ordered the voting to proceed.
Frustrated by the order, all Democrat MPs and some appointed senators walked out of the chamber.
Democrat MPs also placed a wreath in front of the House Speaker's bench in protest before walking out.
Prime Minister Yingluck also attended the parliamentary session and voted in support of the amendment.
The Democrats say that if she submits the bill to the palace, Ms Yingluck may be guilty of acting inappropriately toward His Majesty the King, a serious criminal offence.
The bill is subject to several challenges in the Constitution Court amid claims the amendments are illegal.
The premier has no choice but to submit the bill, as Section 150 of the constitution requires it to be royally endorsed within 20 days of clearing parliament, according to Apiwan Wiriyachai, a Pheu Thai MP for Nonthaburi Apiwan Wiriyachai and member of the party's political strategy committee.
The bill would become law only after it receives royal endorsement from His Majesty and is published in the Royal Gazette.
Mr Apiwan said Pheu Thai's legal team had studied the case carefully and concluded that legislative procedure must be followed.
The legal team believes the charter court has no authority to accept for consideration several petitions which cite Section 154 of the charter as a reason to halt the bill, he said.
The section stipulates that "any bill" which passes parliament must be submitted to the Constitution Court if more than one-tenth of MPs petition the parliament president, Senate president, or the House speaker that the bill breaches the constitution.
Mr Apiwan said the legal team believed Section 154 covered only general or organic bills, not charter changes.
But the opposition and the Group of 40 Senators insist the "any bill" stipulation in the section also covers charter amendments.
Pheu Thai list-MP Phichit Chuenban, a member of the party's legal team, noted that even though the Constitution Court had earlier accepted petitions against the charter change bill, the court had not ordered an injunction to suspend the third reading.
There was therefore no reason to stall the legislation, he said.
On Wednesday, the Constitution Court accepted two separate petitions filed against the charter amendment bill for consideration.
PM's Office secretary-general Suranand Vejjajiva said the prime minister could not afford to violate the constitution.
"If the prime minister fails to submit the bill, she will breach the charter," he said.
But Democrat leader Abhisit Vejjajiva on Friday urged Ms Yingluck to think carefully before submitting the bill for royal endorsement. She should wait for a Constitution Court ruling on the matter within 20 days to avoid any legal complications that may ensue, he said.
The Constitution Court on Friday voted to accept another two petitions filed against the charter amendment bill. They were lodged by Senator Sai Kangkawekhin and Democrat list-MP Pirapan Salirathavibhaga.