It will set-up an inquiry to "fully investigate the matters raised by the petition", health committee chair Simon O'Connor said.
The terms of reference will be drafted over the next few weeks, which will form the outline of that investigation.
"This is an important subject and the committee needs to think carefully about the best way to examine it," Mr O'Connor said.
"I would like to see a thorough investigation that covers as many aspects of this topic as possible in a responsible and robust manner."
Act's David Seymour, Green Party MP Kevin Hague, Labour's Iain Lees-Galloway and Chris Bishop of the National Party joined Ms Street in receiving the signatures on the steps of the Parliament Buildings in June.
Ms Street, who previously introduced the unsuccessful End of Life Choice Bill, said at the time the new petition did not ask for a bill, although there was "a perfectly serviceable" one available already.
"It asks for an inquiry into public opinion on the issue of assisted dying in certain circumstances -- terminal illness and irreversible conditions that make life unbearable."
Efforts to change the law have previously been made through the introduction of members' bills.
They failed in conscience votes at the first reading stage - meaning the issue did not go before a select committee, where facts including overseas evidence can be closely reviewed.
Former NZ First MP Peter Brown's "Death with Dignity" bill was narrowly defeated in a conscience vote 60-58 in its first reading in 2003. Prime Minister John Key voted for that bill, as did current MPs Murray McCully, Maurice Williamson, David Cunliffe, Ruth Dyson, Phil Goff, Winston Peters, Pita Paraone and Metiria Turei.
A previous bill, championed by Michael Laws in 1995, failed by 61 votes to 29.
Ms Street's Bill failed to be selected for 18 months before being withdrawn late in 2013 after a lack of support from her colleagues.
The End of Life Choice Bill would have allowed certain New Zealand residents aged 18 or over, such as those with a terminal disease or physical or mental condition that makes life unbearable, to have assistance to die.