The 6'5", 18st 1lb (115kg) loose forward has played a prolific role for the Mayfield club in three senior seasons and was part of the club's 2012 British & Irish Cup campaign, having helped Dundee to a second-placed finish.
Interim Edinburgh Rugby head coach, Stevie Scott, said: "We keep tabs on a lot of Scottish Premiership players and, after winning the player of the season award last year, have been well aware of Richie's potential.
"He's backed that up with consistently good performances for Dundee this season and so has merited the opportunity to train at Murrayfield and allow us to have a closer look at him for the rest of the season."
McIver has enjoyed a rapid rise through the domestic ranks in his early 20s, having joined Dundee from Caledonian regional division two side, Harris, in 2010, before working his way into the first team, from bit part player to stick on starter.
Richie McIver (25) - back-row
DOB: 18 July 1987
Height: 6'5" (198cm), weight: 18st 1lb (115kg)