Doumbia arrives from CSKA on a permanent basis for 14.4m.
"Every player we buy is after a long process of observation," Baldissoni told Roma Radio.
"[Seydou] Doumbia we've followed for at least three years, and have spoken to CSKA Moscow several times to try and get him.
"His numbers speak for themselves, and he'll do the same in Rome, I'm sure of it.
"There are a lot of players who we follow, and when the conditions are right we make a move."
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