The pair will aid Presiding Officer Alison Johnstone herself elected on Thursday, in her duties and will chair some parliamentary debates.
In a marathon process that took more than five hours on Friday, SNP MSP Ms Ewing won the first vote after four rounds, ending up on 64 votes, while Liberal Democrat Mr McArthur saw off the competition in just two rounds of voting, finishing with the backing of 74 fellow MSPs.
An attempt was made by Labour MSP Daniel Johnson to speed up the process by changing to the single transferable vote (STV) voting system, which would see MSPs rank their preferences for the position as opposed to voting over multiple rounds.
But the idea was blocked by the Presiding Officer, who pointed out it would be unfair given one of the contests had already been completed – although she did say she would be open to such a move for future votes.
A total of ten MSPs sought election to the role on Friday, in contrast to Ms Johnstone being the only candidate for the Presiding Officer role on Thursday.
As a result of her ascent to the role, Ms Johnstone was forced to relinquish her party affiliation and act in a nonpartisan way for the duration of her term.
Her deputies do not have to give up their party affiliations.
Ms Ewing had been one of five MSPs from the governing party that initially put themselves forward for election.