Odemwingie was reported to have injured his thigh while on international duty with Nigeria whilst Mulumbu was in doubt even before he joined the DR Congo for his international obligations.
But Baggies boss Roy Hodgson says the pair will be fine to take on his former club at The Hawthorns on Saturday.
"Peter is okay, he came back and trained yesterday, as did Mulumbu - it was good to have them back," Hodgson told West Brom's official website.
"They've got a day off to rest, which they probably need as they both travelled. So, by Thursday they'll be fully fit."
"Morrison stayed back an extra day before travelling to join up with Scotland,” Hodgson added.
"He had the stitches out on Monday. It's a nasty wound and he now has a big black eye because the blood has come down from the wound.
"He looks worse than he is, but he's fit and trained yesterday."
On Dorrans’ ankle injury: “Graham is improving. It's positive but we can't put a date on his return.
"At the end of last week it looked less positive than now, which is good news.”