The process got underway at the King's Hall in Belfast on Monday morning, but the first preference votes for the ten candidates were only declared in the evening after long delays.
Counting at the venue was eventually adjourned in the early hours of Tuesday morning and will restart at 9am, postponing the announcement of the final results by a day.
With the quota set at 156,532, Ms Anderson was elected with 159,813 votes - a first preference share of 25.5%.
Speaking to UTV after she was returned as MEP, she said: "I'm absolutely overwhelmed by the size of the vote and I want to thank all of the voters individually who put a '1' beside my name for our party.
"This is an endorsement of Sinn Féin's contribution to the peace process and I think talking to many voters throughout the six counties, there was a real sense of ownership of this peace process and they wanted to see us continue to develop as we had been doing.
"They also want to see us change society, [in relation to] austerity and cuts and they know quite clearly that I was the only MEP from the north who voted against the cuts."
Five other candidates are still in the battle for Northern Ireland's remaining two seats in the European Parliament.
NI Conservatives candidate Mark Brotherston was eliminated with just 4,144 first preference votes, before the Green Party's Ross Brown, Tina McKenzie from NI21 and UKIP's Henry Reilly were excluded from the race.
Sitting DUP MEP Diane Dodds came second in the poll, securing 131,163 first preference votes, while the UUP's Jim Nicholson has 83,438.
They both depend on transfers to be elected.
Ms Dodds is certain to take the second seat after the DUP saw its share of first preference votes rise by 2.7% since the last European election in 2009.
Fellow outgoing MEP Mr Nicholson is likely to take the third seat, although the contest is closer than he would have liked.
The other remaining candidates are the SDLP's Alex Attwood, TUV leader Jim Allister and Alliance's Anna Lo.
The Alliance Party has increased its first preference share, securing 7% of votes, while the SDLP saw its share decrease to 13%.
Mr Allister, who championed an anti-Europe message during the campaign, performed well, receiving over 12% of the first preference votes.
The full details of the first preference votes for each candidate are available here.
The turnout has already been established at 51.84% - up on the last European poll in the region.
Of an eligible electorate of 1,226,771, there were 636,093 votes polled. A total of 9,968 papers were rejected, leaving 626,125 valid votes.
The poll took place last Thursday, at the same time as Northern Ireland's local government election.
The count is being conducted using the single transferable vote method.
Chief electoral officer for Northern Ireland Graham Shields said the requirement to recount all Mrs Anderson's ballots in order to distribute her surplus had not been anticipated.
"We knew we were here for a long day and we potentially expected to be here if we needed to be into the early hours of the morning but I don't think anybody could have reasonably foreseen that a count would have run into two days, for 24 hours," he said.
Mr Shields said the episode underlined the need for electronic vote counting in Northern Ireland.
Meanwhile in Great Britain, UKIP have topped the European poll.
The party has returned 24 MEPs. Labour is next with 20 MEPs, while the Tories have limped in third with 19 seats.