Senator Lines is the first Labor woman to hold the role of Senate president, and only the second woman after the Liberals' Margaret Reid held the position between 1996 and 2002.
"Thank you very much senators for the honour and privilege bestowed on me here today," she told the Senate after her election.
"I'll do my utmost to be a fair and consultative president."
Leader of the Government in the Senate Penny Wong told the chamber Senator Lines was "appropriately qualified and suited to the significant responsibility that comes with occupying the chair".
"It's taken a long time but I'm pleased that we see yet another woman serving in this high office," Senator Wong said.
"I'm confident Senator Lines will represent the interests of the Senate and the parliament as a whole, particularly when it comes to matters of privilege."
Leader of Opposition in the Senate Simon Birmingham also congratulated Senator Lines after she received the support of the coalition.
"There are duties that also falls upon each and every one of us in our conduct that we bring to this place," he told the chamber.
"I hope that all senators will work to make sure that you (Senator Lines), the deputy and those who hold the chair from time to time are all supported as much as possible."
The 47th parliament sat for the first time on Tuesday, with lower house colleagues invited into the Senate chamber by the deputy of the governor-general to witness the declaration of parliament opening.
Senators from all states and territories were subsequently sworn in and asked to recite the oath of allegiance before signing the Test Roll and the Senators' Roll.
The West Australian senator has served as deputy Senate president since 2016 and replaced the Liberals' Slade Brockman in the top job with 54 votes.
The Greens nominated WA Senator Dorinda Cox for president. She received 12 votes.
Two informal votes were recorded.
Speaking after her nomination, Senator Cox called for more diverse representation in the Senate.
"Never in this country's colonised history has a First Nations person ever been appointed as the president of the Senate," she said ahead of the ballot.
"At a time where more First Nations representation is here in the 47th parliament than ever before, it's now our chance to take that further step and realise the full ambition of our First Nations parliamentarians.
"Australians told us they wish to see a different parliament. They made it clear their parliamentarians don't just talk about their communities but they should look like them, sound like them and they should be from those communities."
One Nation leader Pauline Hanson attempted to put forward WA Senator Glenn Sterle but the standing orders prevented her from moving the nomination with Senator Sterle not present in the chamber.
Senator Lines filled a casual vacancy in the Senate in 2013 before being re-elected in 2016 and 2022.
The senator, who hails from Labor's left faction, is also known for her pro-Palestine stance, branding Israeli policies as "apartheid".
She has also been a strong advocate for Indigenous people and education reform.
Twelve incoming senators are expected to deliver their maiden speech in the first sitting fortnight, including former Wallabies player David Pocock, the first hijab-wearing Muslim woman in parliament Fatima Payman, and the sole United Australia Party representative Ralph Babet.
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