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.
Senator Lines promised to "carry out the role of president in an impartial way".
"I look forward to you putting your trust and support in me," she told the Senate.
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.
The Albanese government is set to introduce 18 pieces of legislation this week, including a bill covering its 43 per cent emissions-reduction target for 2030.
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.
The Greens hold the balance of power in the Senate, with the minor party and an independent or senator from One Nation, the Jacqui Lambie Network or UAP needed to make up the magic number of 39 needed to pass legislation if the opposition is not forthcoming.
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