Left-back Wallace, 23, will join Rangers for a fee of £1.5 million after he passes a medical and completes the formalities of the transfer.
Goalscoring midfielder Bedoya, 24, will join when his contract expires at the end of the Swedish season provided he is given a work permit.
Wallace will be eligible for the Champions League qualifier against Malmo if he completes his move prior to the UEFA deadline of 23:00 on Thursday.
"We’ll be very pleased to get a player," Smith told STV. "We have been working on quite a few.
"We just wanted to get players in as we are trying to build squad and we are trying to help the manager build for the new season."
Wallace has won five caps for Scotland.
Bedoya has picked up 13 caps for the US since 2010 and is expected to be awarded a visa with his country ranked 24th in the world.
Rangers had tried to sign him immediately but saw their cash offer rejected, so have instead opted to use the Bosman ruling to their advantage.