The ex-Kaizer Chiefs boss will return to the Bafana hotseat after seeing out the season with Matsatsantsa, who tonight start their CAF Confederation Cup Group D campaign against Guinea's Horoya AC at Lucas Moripe Stadium (19h00).
"It's good for him [Baxter], it's also good for his career," Alexander tells snl24.com/kickoff.
"I can only describe it as a bitter sweet moment, because as much as we loved him at the club, this is his career. It's a big opportunity for him, we wish him great success as national team coach."
Meawhile, Alexander is unsure when he will return to action after already spending a month on the sidelines with a fractured metatarsal.
"I have started with light training, but not with full training yet. I can't say when I will be back on the field but I will feel when it's okay. I won't force it, I will wait until I'm a hundred percent fit."