Mr Varadkar added that he was "proud that we have made the country a more equal and more modern place when it comes to the rights of children, the LGBT community, equality for women and their bodily autonomy".
During his time as taoiseach, Mr Varadkar championed referendums to change the Irish constitution legalising same-sex marriage and abortion.
Mr Varadkar also listed work to improve the affordability of childcare among his achievements as well as increasing government spending on arts and culture, international development, and public infrastructure.
He also conceded that "there are areas where we have been much less successful" but added: "I hope you'll forgive me if I leave it to others to point them out on a day like this."
Mr Varadkar said his reasons for stepping down were "both personal and political".
He said that he felt the current government "could be re-elected" but he felt he was "not the best person for the job anymore".
The Irish government parties have said they do not expect Wednesday's announcement to trigger a general election.
In the election of 2020, Mr Varadkar led his party to a third-place finish in terms of number of seats in Dáil Éireann, the lower house in the country's parliament.
As part of the coalition deal struck between the parties it was agreed that Mr Varadkar and Micheál Martin would each hold the position of taoiseach for two years.
In 2020, Mr Martin was appointed taoiseach with Mr Varadkar serving as his tánaiste (deputy PM), before the two swapped roles in 2022.
Speaking after Mr Varadkar's resignation announcement, Mr Martin said he had been "surprised" by the decision.
"I want to take the opportunity to thank him sincerely, we got on very well," Mr Martin added.
Mr Martin said he remained committed to fulfilling the full term of the coalition government.
Eamon Ryan, leader of the Green Party, the smallest of the three coalition partners, said Mr Varadkar had been "an energetic and committed leader of the country who was always supportive of his government colleagues".
Mr Ryan said his party looked forward to the Fine Gael leadership contest and the election of a new taoiseach.
In the interim, he said, the government would continue to fulfil its mandate.
"I would like to offer my good wishes to Leo as he prepares to depart the taoiseach's office," he added.
Speaking in the Dáil, (lower house of Irish parliament) Sinn Féin President Mary Lou McDonald, who is leader of the Opposition, called for a general election.
She said it was "unthinkable" for the next taoiseach to be chosen by a "conclave" of Fine Gael politicians.
"This is a time for fresh leadership. Not just a change of taoiseach, but a change of government, and a change of direction," she said.
Ms McDonald claimed that when Fine Gael took power in 2011 Ireland had one of the highest levels of home ownership in Europe, but it had since declined to one of the worst.
"This government has now run out of steam and run out of road, so rather than limping on in a caretaking capacity let's go to the people," she said.
The UK Prime Minister, Rishi Sunak, wished Leo Varadkar well following his resignation.
A spokesperson said the PM would "work closely with him and his successor".
"Ireland is a vital partner of the UK," the spokesperson added.
Northern Ireland's First Minister Michelle 'O'Neill also said it was "time for an election" in the Republic of Ireland.
"Now is not a "time for the rearranging of the deck chairs," the Sinn Féin vice president said.
She described Fine Gael's time in power as "13 years of failure".
Deputy First Minister Emma Little-Pengelly said: "Leo Varadkar and unionism didn't often see eye to eye, if at all".
However, the Democratic Unionist Party MLA wished him "all the best".
DUP Leader Sir Jeffrey Donaldson said he and Mr Varadkar "were very often on different ends of the political spectrum".
"We differed on the Republic of Ireland's approach to legacy, and sharply differed on his approach and attitude on the [Northern Ireland] Protocol and the constitutional future of Northern Ireland," he said.
"Where we differed, we did so respectfully."
Sir Jeffrey added that there were other areas where they worked together on matters of mutual benefit "for both our countries".
Ireland's President Michael D Higgins was told of the taoiseach's intention to resign shortly before Wednesday's press conference and the pair spoke immediately afterwards.
A spokesman for the president said: "Over the course of this, the president thanked the taoiseach for his service."
Source: BBC
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