The board has been established following an independent review of the professional game in Wales.
It will comprise representatives from the Welsh Rugby Union (WRU) and Wales' four professional regions - Cardiff Blues, the Scarlets, Ospreys and Newport Gwent Dragons.
The board's first meeting is due to take place later this month.
WRU group chief executive Roger Lewis said: "We are delighted to announce the appointment of someone of Sir Wyn's calibre as the inaugural chair of the PRGB.
"His status as a High Court judge ensures he takes on this post with a formidable reputation for objectivity, fairness and an undoubted ability to find intelligent solutions to complex problems."
The appointment was welcomed by Scarlets chief executive Mark Davies, speaking on behalf of the four regions.
"The scale, scope and role of the new PRGB, and the clear aims that we have set out, mean that we need a very considerable individual indeed to be able to share the responsibility and lead the discussions that result in us collectively achieving our objectives for a healthy and sustainable future for Welsh rugby," he said.
"Sir Wyn's knowledge and passion for Welsh rugby, together with the scale and degree of judgement he employs daily at a very profound level, means it is a role clearly well within his capability and experience."
- Welsh Rugby Union
- Newport Gwent Dragons