Luton have signed former Peterborough and Brighton striker Craig Mackail-Smith on a two-year deal.
Norwich City have completed the signing of goalkeeper Jake Kean following his release from Blackburn Rovers.
The 20-year-old striker impressed during a loan spell at MK Dons during the first half of the season, scoring 16 goals in 29 appearances, and agreed to join the Rams after talks with manager Steve McClaren.
Bamford's loan spell will be effective from Monday, 6 January, meaning he will not be eligible to make his Derby debut against his parent club when they meet in the FA Cup third round on Sunday.
A Derby statement read: "After meeting head coach Steve McClaren, Bamford has agreed to bolster the Rams' attacking firepower for the rest of the season and is expected to be in contention to make his debut in next Friday's Sky Bet Championship game away to Leicester City.
"Bamford is to become the fourth England U21 international in Derby's squad, alongside academy product Will Hughes and loanees Andre Wisdom (Liverpool) and Michael Keane (Manchester United)."
Grantham-born Bamford came through the ranks at Derby's East Midlands rivals Nottingham Forest.
He made two first-team appearances for the Tricky Trees at the age of 18 during the 2011/12 season, and within a month had joined Chelsea on a five-year deal.
Bamford had two loan stints with MK Dons and his fine scoring form earned him the League One Player of the Month award in October.
Bamford represented England at both U18 and U19 level and was handed his first U21 cap by head coach Gareth Southgate in November's 9-0 rout of San Marino.