Chief executive Gary Hetherington said: "Stuart's appointment recognises his outstanding contribution to our academy system and also indicates the direction we want to Tykes to head."
Davies resigned as director of rugby on April 30 with Leeds already relegated from the Premiership.
The Tykes, who narrowly escaped the drop last term, finished 13 points adrift at the bottom of the table, paving the way for Davies' departure.
Leeds have been credited with having one of the most successful academies in the Premiership with Lancaster overseeing its development.
And although his CV is short on coaching at senior level, Hetherington is convinced he is the right man for the job.
"Stuart has proved to be a top-class manager and coach with drive and enthusiasm," he said.
"I don't believe Stuart's lack of experience at this level is a problem because he has many personal qualities.
"He also has a very talented coaching group and senior management team who are delighted with his elevation.
"We will rebuild the Tykes team using the talent and strength of our academy system, a number of quality signings and a team spirit and work ethic which will be hard to beat."
Lancaster, who was born in Penrith in Cumbria, is excited by Leeds' focus on youth development as they target an immediate return to the top flight.
He said: "With my appointment the club have made a bold statement as to the future direction they would like to take and it is one I firmly believe in.
"By growing the club through an academy system that develops players from the Yorkshire region, it will create a culture and a pool of talented players that will provide the club with a long-term and sustainable future."