Following the party's election, "Rishi Sunak is therefore elected as leader of the Conservative party," senior backbencher Graham Brady said, as rival Penny Mordaunt vowed her "full support" for the former finance minister.
"These are unprecedented times. Despite the compressed timetable for the leadership contest it is clear that colleagues feel we need certainty today," Mordaunt said in a statement.
Sunak's path to 10 Downing Street was make more clear over the weekend when former party leader and PM Boris Johnson announced he wasn't in the race to get his post back.
The Tories have been forced into their second leadership contest since the summer due to PM Liz Truss's resignation after only 44 days following the disastrous market response to her tax-slashing mini-budget.
She had replaced Johnson in early September following another government revolt over a slew of scandals, most notably the "Partygate" controversy involving Covid lockdown-breaching parties.
Meanwhile, as the Conservative "Tories" tumble, the main Labor opposition, which has opened up huge poll leads after Truss's government saw the Conservatives' popularity plummet, is demanding a general election.
"Tory MPs are set to hand Rishi Sunak the keys to No 10 (the prime minister's official residence) without him saying a single word about how he'd govern," tweeted Angela Rayner, deputy leader of the main opposition Labor Party.
Under the UK electoral system, there is no requirement for a general election if the leader of the party in power changes.
With Sunak seen as bringing stability to financial markets, sterling rose and yields fell Monday.
"Investors clearly hope Sunak will stabilize the economy and the political situation -- though it's hard to work out at this point which is the harder task," said AJ Bell financial analyst Danni Hewson.
Sunak, the UK's first person of color to be Prime Minister, was born in the UK but his parents, of Punjabi heritage, came from Africa. His father was born in what became independent Kenya, while his mother was born is what is now Tanzania.