The 23-year-old USA international has been linked with Rangers in the past but Birmingham will take first look.
Bedoya looks likely to run down his current contract with Swedish side Orebro and said: 'I am happy and grateful for this opportunity and it will increase my experience, motivation and confidence for the future.
Gaining experience: Bedoya is relishing his stint at St Andrew's
'Hopefully I can show that I have the qualities necessary and see where I stand in comparison to some of the best players in the strongest league in the world.'
Bedoya, a central midfield player, earned his first international start against Brazil last August after narrowly missing out on USA's World Cup 2010 squad.
Orebro sporting director Magnus Skoldmark said: 'It's fun that a Premier League side shows interest for one of our players, it shows that we have a good professional environment.'
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