Chamberlain has been at the club for four seasons having previously worked for Fulham in the Premier League.
Paris-born Kamara has started just five league games for Fulham this season, scoring once, and struck against CSKA Sofia in the Europa League.
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Suddenly, every set-piece was a great opportunity for Fulham to take advantage of a West Brom defence which had not previously played together.
At that stage, things looked grim for Fulham but they were soon back in the tie thanks to a huge slice of luck.
Ronnie Wallwork's shot then caused further consternation for Fulham as it was parried by Van der Sar and Earnshaw was only just unable to convert.
The success continues a sensational second European campaign for Fulham, who had eliminated defending champions Shakhtar Donetsk and favourites Juventus in the previous two rounds.
Barry Hayles will return for Fulham, meanwhile, after a three-game suspension.
For Fulham and their fans, it was the perfect start as the Cottagers raced out of the blocks to stun Shakhtar and take an early lead.
Andy Johnson had a header cleared off the line for Fulham, while Hull keeper Matt Duke saved from long range Paul Konchesky and Clint Dempsey strikes.
"I am pleased that we have been able to reach an agreement between the two clubs to enable me to play for Fulham next season, " added Davis.
The Clarets' fearless passing approach has already accounted for Fulham, Chelsea and Arsenal in their run to the last four - and they surprised Spurs with that early strike.
Johnson's injury will be a headache for Fulham manager Roy Hodgson, who opted to field the striker alongside Bobby Zamora in an unchanged line-up from Saturday's league win over Portsmouth.
Arsenal's fluid one and two-touch passing bewildered their opponents and damage limitation already appeared to be the order of the day for Fulham, as they defended deep and in numbers.
We've been written off all the way through (the competition) and I'm sure we'll be written off in the final, but we'll push on and hopefully create even more history for Fulham.
Perhaps the best chance of all for Fulham fell to Simon Davies, who was through on goal but saw his shot from 10 yards superbly deflected over the bar by the foot Benaglio.
But the goal merely proved a wake-up call for Fulham, who reasserted control over proceedings and then stretched their lead as a 15-pass move ended with Gera applying a first-time finish to Kelly's cutback.
Shakhtar sent on Douglas Costa and he twice went close before Schwarzer pulled off a fine fingertip save to deny Fernandinho in stoppage time to preserve for Fulham the slenderest of advantages going into the second leg.
There was more trouble for Fulham before the break and it was no surprise to see Johnson receive his second booking of the half - and subsequent red card - for yet another late tackle, this time on Neill.
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Roma boss Claudio Ranieri believed the red card for Nevland was a turning point in the game but a deserved punishment for the Fulham striker.
Fulham manager Roy Hodgson was understandably keen for his team to avoid a road trip and claimed the 1, 140-mile round trip would be a "disaster" for the 2, 500 Fulham fans who have bought tickets for the game.
Duff, 31, Treacy and O'Dea have been back in action for their clubs Fulham, Preston and Ipswich respectively but Andrews has yet to return for Blackburn.
Gianfranco Zola's team led through Carlton Cole's first half goal and looked set for victory as Fulham's South African midfielder Kagoshi Dikgacoi was sent off in his first start for the club.
It provided the platform for a late Fulham surge, capped by Pearce's deflected 18-yard shot that left James wrong-footed.
"We are delighted to announce that we have reached agreement with Fulham for the transfer of Mousa Dembele, " Tottenham announced on their website.
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He played 584 matches for English clubs Fulham and West Bromwich Albion, then began a managerial odyssey that took him through Canada, Spain, Portugal and the Netherlands.
He went on to represent his country and play in the Premier League for Blackburn and Fulham before his career was cut short by a car accident.
The last quarter of the match saw Fulham pressing for a winner with Wolves, who also picked up several yellow cards, offering the odd threat from set pieces and on the break, but neither side could force a breakthrough.
The match against Fulham is scheduled for 1500 BST on 16 August at the KC Stadium.
The Cottagers failed in an attempt to have Pascal Zuberbuhler registered for the match, which Fulham won 1-0, after an injury crisis at the club.
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