Rams boss George Burley has been determined to bolster his squad in readiness for a relegation battle and has brought Vincent and Reich to Pride Park.
Vincent joins the struggling First Division club on a free transfer from Portsmouth after being deemed surplus to requirements at Fratton Park.
The 28-year-old has spent the past three months on loan at Walsall, with Burley having been impressed by his displays with Derby's Division One rivals.
German forward Reich has been on trial with The Rams this week and has shown sufficient ability in training to warrant a contract.
Reich arrives in the East Midlands from Werder Bremen and will be charged with the onerous task of scoring the goals to keep Derby in the First Division.
Burley is hoping Reich's versatility and experience will prove beneficial to the club's cause during the closing months of the campaign.
"Marco has impressed us," said Burley.
"He was recommended by an agent and so it was a case of checking his credentials, doing our homework and getting the player down here so we could have a look at him.
"He can play either side of midfield, or up as a striker. He has good pace and will add quality and experience to our squad."
Meanwhile, teenage goalkeeper Lee Camp has signed a two-and-a-half year contract extension with The Rams this week while defender Chris Palmer has joined Conference club Hereford United on a month's loan.
