The Spanish side confirmed the move on their official website. Celtic earlier signed Nigeria international defender Efe Ambrose from Israeli side FC Ashdod on a three-year contract.
Fedor, also known as Miku, is a Venezuela international who was Getafe's top goalscorer last season.
The 27-year-old joined Getafe from Valencia in 2010 having spent most of his time with the club out on loan.
Nigerian international and Olympic silver medal winner Ambrose has spent the last three years playing for FC Ashdod in the Israeli top flight.
Speaking to the club's official website, the 23-year-old said: "It has been a long day, but it has been worth it. Today is one of the happiest days of my life, signing for one of the biggest clubs in the world - a club I have known about since I was young.
"I just can't wait to get started, to play in front of the fans and call this place home. I would like to thank God for everything and to thank the manager and directors here at Celtic - who have placed their trust and confidence in me.
"The move to Israel really opened the door for me and gave me my opportunity. I had been to other clubs, but they were the ones who gave me my chance. For that I would like to thank the coaches and directors at FC Ashdod, my agent Dudu Dahan and also my colleagues and the fans - who all helped develop me as a player."
Ambrose plays at centre-back or along the back line, but insists he has no preference.
He said: "I am the kind of player who plays where it is of benefit to the team. If the manager trusts me to play in midfield or defence, then I trust him and I am the kind of player who will give 100%, whatever the coach asks of me."
Portsmouth have signed defender Josh Thompson on a month's loan from Celtic, subject to international and FA clearance.
The 21-year-old, who was on trial with Pompey earlier this summer, has not arrived in time to feature against Oldham on Saturday.
Ryan Stevenson has rejoined Hearts on a three-year deal.
The attacking midfielder has made the shock return to Tynecastle just months after quitting over a dispute over unpaid wages and signing for Ipswich in January.
He will be available for selection for Sunday's Clydesdale Bank Premier League game against Dundee.
Before his acrimonious exit, Stevenson enjoyed a successful period at Hearts, previously appearing in 74 competitive matches and scoring 11 goals.
He told Hearts website: "I'm excited at the prospect of returning to the club.
"Naturally, the circumstances of my previous departure might have made this move seem unlikely but I want to assure everyone that I am only focused on playing and winning with Hearts. I am delighted to be here."
Boss John McGlynn said: "I am delighted that we have re-signed Ryan.
"He is a quality player and can be used in a number of roles. He's physically strong and will be an asset to this Hearts team.
"When I heard he wanted to return it was a simple decision for me to make. He gives us more options and that is to be welcomed."
Hibernian have signed Northern Ireland international Ryan McGivern on loan from Manchester City.
The 22-year-old left-sided defender, who has 16 full caps, has joined the Easter Road club until January.
McGivern has made one appearance for City, as a substitute in a 5-0 league win over Sunderland in April 2011.
But he has played 75 first-team games in loan spells with Morecambe, Leicester, Walsall, Crystal Palace and Bristol City.
McGivern said: "I'm just really excited about playing for Hibernian and helping the team to do well in the SPL.
"Obviously growing up in Northern Ireland I'm well aware of what the SPL is all about - it's a good, competitive league with passionate supporters.
"Hibs have enjoyed a decent start to the SPL season so far; I'm looking forward to be able to help to build on that start."
Defender David Stephens earlier left Hibernian to join npower League Two club Barnet.
The 20-year-old made 29 appearances for Hibs in two years after joining from Norwich.
But the Wales Under-21 international was out of favour under manager Pat Fenlon and has been allowed to leave.
Everton have signed Kilmarnock winger Matthew Kennedy for a nominal fee.
The 17-year-old has agreed a three-year deal with the Barclays Premier League club, after impressing in the Clydesdale Bank Premier League.
Kennedy, who made his debut against Hibernian at the age of 16, has represented Scotland at under-15 and under-16 level.
Newcastle United defender Paul Dummett has joined St Mirren on loan until January.
The Wales Under-21 left-back will go into the Saints squad for the Clydesdale Bank Premier League clash with Aberdeen at Pittodrie pending international clearance.
Dummett, 20, was loan to Blue Square Premier League side Gateshead last season.
Buddies manager Danny Lennon said: "I first came across him a year ago but I got a call yesterday afternoon which reignited interest. It works well for both parties and I am delighted."
Lennon also confirmed that he is looking at Franco Miranda with a view to offering him a deal.
The versatile 27-year-old Argentine, who previously enjoyed a two-year loan stint at the Paisley club, is a free agent after leaving Patronato. Lennon said: "We will look at him for the next week to 10 days."
Aberdeen have released forward Michael Paton.
The club confirmed they had reached agreement with the striker and completed the paperwork just before the 11pm transfer deadline, allowing Paton to find a new club.
The 23-year-old, a product of the club's youth academy, made 57 first-team appearances for the Dons and had loan spells at Brechin and Stockport.