Australian captain Finch, who steered his country to its maiden T20 crown in the UAE last month, has missed the start of the BBL season because of lingering knee soreness.
It follows knee surgery that allowed the 35-year-old to play at the World Cup, where he averaged 19.28 across seven innings, with a top score of 44 against England.
The second-highest run-scorer in BBL history, Finch will bolster the Renegades' inexperienced top order after their slow start to the season with the bat.
Having finished last in the previous two campaigns, the Renegades won a nail-biting opener against Adelaide on the final ball, before suffering successive defeats to the Strikers and Brisbane Heat.
The Renegades again find themselves last on the table ahead of Wednesday night's clash with the Scorchers at Marvel Stadium.
"The last couple of games, batting second, a little bit of inexperience probably creates a bit of chaos at times," Finch said.
"(Mackenzie) Harvey has started off beautifully and the way Zahir (Khan) has joined the group and done really well has been really impressive.
"But you couldn't ask for a huge amount more from a really young group of guys who haven't played much T20 cricket.
"(When your top six is inexperienced) you're always going to have your back against the wall but it's something that we knew was going to happen a few weeks ago.
"The way the boys have embraced it and taken on the challenge has been really impressive."
Finch hasn't done a lot of running in recent weeks but had a hit in the nets on Friday and trained again with the Renegades at Junction Oval on Monday.
"(The recovery process) was just hampered by the World Cup," he said.
"We pushed really hard to get back for that and it was a risk well worth taking, but it just probably needed a little bit more time.
"From the end of the World Cup to now has been a good, solid month of rehab, which has helped.
"I'll hit a lot of balls in the next couple of days and I'm feeling good at the moment.
"The skill acquisition part of it is something that I don't think needs a huge amount (of attention) - at 35 years old I think there's a decent base to fall back on."
Fast bowler James Pattinson (general soreness) is a chance of returning from injury on Wednesday night, while Shaun Marsh (calf) won't play in the first of two matches against his former team.
Marsh is undergoing a rehabilitation program in Perth and is expected to join Finch at the top of the order later this month.
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