The 29-year-old loose-head first joined the club as an apprentice in 2004 and made 55 appearances before moving south of the border for spells with Gloucester and Sale Sharks.
"I'm delighted to have signed a new deal for Edinburgh Rugby and to return to Scotland," he said.
"I've learned a huge amount from my time in the English Premiership and believe I'm coming back to the club a completely different and much improved player.
"I'm looking forward to putting that into practice for the club who gave me my first chance in professional rugby, alongside some quality players in the front row."
Dickinson is the third international signed by the club for next season, with Tongan hooker Aleki Lutui and Scotland wing Nikki Walker also committed to moves to Murrayfield this summer.
Interim head coach Stevie Scott said: "Alasdair is a quality, international rugby player in a key position. He's someone I've worked with for a long time, bringing him from Gloucester to Sale for two years, and am now looking forward to working with him again.
"He does everything by the book to get the best out of himself and what he can contribute to the team so, from that point of view, he will be a great addition to Edinburgh Rugby next season."
Meanwhile, record appearance holder Allan Jacobsen will start his last match against Newport Gwent Dragons at Murrayfield on Friday night.
Scotland's most-capped prop will retire after 285 club appearances as he brings down the curtain on a 16-year Edinburgh career.