A drawn-out recheck of the count, called for by Mr Ryan, found no major errors and the Green Party leader eventually conceded defeat last night.
Independent candidate Ms Childers took the second seat and Fine Gael’s Brian Hayes took the third.
The disappointing end for Mr Ryan came after Ms Childers made a shock comeback in the race early on Monday morning, after securing 12,458 transfers from Fianna Fáil candidate Mary Fitzpatrick.
Ms Childers is the daughter of former Fianna Fáil president Erskine Childers, a point widely recognised by voters during the election campaign.
As the outgoing MEP was elevated into second place during the gripping count, Mr Hayes and Mr Ryan were pushed back and left with just 1,149 votes between them.
Mr Ryan then asked for a recheck, which involved bundles of votes being checked as opposed to a full recount.
By yesterday evening, Dublin returning officer James Barry said only “minor discrepancies” were found and confirmed the original winners.
This included Sinn Féin’s Lynn Boylan, who topped the poll on the third count with 89,764 votes, a large chunk of the 352,575 valid votes.
Earlier in the weekend, left-wing candidates Paul Murphy, a Socialist Party MEP, and People Before Profit’s Bríd Smith, were eliminated. Their votes helped build up Ms Childers’ position as the count continued.
It was also Labour’s Emer Costello whose transfers helped build up Brian Hayes’s position, when the outgoing MEP was eliminated.
Mr Hayes’ election as an MEP leave a vacant post in the Department of Finance, as well as the need for a by-election in his Dublin South West constituency.
Mr Ryan — despite receiving many transfers from a number of the candidates as they went out during the count — was unable to make up the difference in the recheck and therefore conceded defeat.
The count left the three winners with Lynn Boylan on 89,764 votes, Nessa Childers on 73,598, and Brian Hayes on 73,405.
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