The Welsh Government has said it will invest £3m in Yr Egin, with another £3m coming from the Swansea Bay city deal.
First Minister Carwyn Jones previously told AMs that S4C had promised the move would be at no cost to the taxpayer.
S4C chairman Huw Jones told AMs it was "always clear to us" that the University of Wales Trinity St David as developers would be seeking grants.
The channel's relocation from Cardiff to Carmarthen is at the centre of the university's plan for a creative industries hub.
However, in October, Economy Secretary Ken Skates told AMs it was "disappointing" a funding gap of £6m had appeared, although the university denied it.
Giving evidence to the assembly's culture and Welsh language committee on Thursday, S4C chief executive Ian Jones defended the request for government support.
"If the development makes an economic impact, a linguistic and social impact in the area, that it ticks all the boxes for the Welsh Government, then it follows on naturally that the university would ask the Welsh Government for a contribution," he said.
Mr Jones also defended S4C's decision to pay the university rent in advance for the next 20 years at a cost of £3m.
"We looked at seven or eight different options including taking an equity stake in any building," he said.
"But we decided after scrutinising the project internally and externally that it would give greater assurance to S4C to make a rent-in-advance payment.
"The reason for that is there won't be any rent increases for 25 years - there's no effect in terms of inflation over that period and so we know how much were going to pay."
Meanwhile, University of Wales Trinity St David management have been summoned to give evidence to MPs on the Welsh Affairs committee on 13 March.
Its chairman, the Monmouth MP David Davies, said: "The funding issues surrounding S4C's new headquarters are a concern for the Committee.
"We hope this session will allow Trinity St David to clarify any questions we may have.
"It is essential that public money is spent wisely."
It was "natural" to ask for public funding towards S4C's new headquarters in Carmarthen, the channel has said.