Jenkins, 54, succeeds Mike Ruddock who resigned unexpectedly during the last Six Nations championship after taking Wales to their first grand slam since 1978 in the previous year.
He was given a two-year contract which will take him through next year's World Cup, winning the job ahead of Leeds Tykes director of rugby Phil Davies.
"This is something to which I have aspired for a long, long time," Jenkins told reporters.
"It is a job I would have been disappointed at not filling at some stage of my career I'm very proud and honoured. Im excited at the prospect of working with the Welsh players and I know there are huge challenges that lie ahead of us all as we build towards the 2007 Rugby World Cup.
"I can't wait to get started and I know that the clock is ticking towards my first international in Argentina in 45 days' time. It is a new and exciting challenge for me and I am greatly looking forward to it."
Jenkins said he would not make any drastic changes to the enterprising style which featured during the 2005 grand slam.
"As a Welshman, I believe in the style Welsh rugby is played in. Maybe we need to add a bit of variety and a bit of tactical appreciation."
Jenkins has sought the top job since assisting Alan Davies when Wales won the 1994 Five Nations title. He narrowly missed out two years ago when the WRU appointed Ruddock.
The WRU's five-man selection panel interviewed Jenkins on Wednesday and recommended on Thursday that Jenkins be given the job.
Backrow forward Jenkins was never capped for Wales, but played for Wales A, the Barbarians and Llanelli. He toured Japan with Wales in 1975 and played in Llanelli's famous win over the New Zealand All Blacks in 1972.