Like Parker, Scotland Under-20 second-row forward Robert McAlpine has also signed a two-year deal to join the club on a permanent basis.
Parker is 6ft 8ins and has had one season in the Championship after captaining Haywards Heath.
He said: "I knew that the Edinburgh Rugby coaches had seen some of my tapes so I was delighted to get the chance to meet them and talk about the club's achievements, ambitions and off-field culture.
"It's a massive opportunity for me. To be in the mix with a club like Edinburgh Rugby is really exciting."
McAlpine spent the second half of the season with Edinburgh, making two appearances, after initially signing for Glasgow.
McAlpine said: "It's been great, the players have been really welcoming. It's been easy to fit in as I've played with so many of the younger players at the club during my time in the Scotland age-grades - it's like a home from home.
"This summer will be my first full senior pre-season and I can't wait to push on, build my fitness and physicality, put pressure on the other second-rows and see what progress I can make."
Edinburgh head coach Michael Bradley explained the thinking behind the signings.
He said: "While we'll continue to refine the expansive, attacking play for which the club is famous, we're keen to introduce a harder, more aggressive edge to our play, and believe this pair will work tirelessly to lay the platform from which our back division can play."