Felgate, who coached British number one Tim Henman for 10 years until the pair split in 2001, succeeds Frenchman Patrice Hagelauer who resigned in December after four years in the post.
Commented Felgate: "I am very excited to have this opportunity in what I consider to be one of the top jobs in world tennis, not just in Britain. I believe that Patrice has implemented some lasting reforms.
"But of course I will have my own ideas on how we get the best out of our national training department and the players themselves."
Added LTA chief executive John Crowther: "This is a key role in British tennis and I am certain that David is the best person to build on the foundations laid by Patrice over the last four years."
