Player-manager Dennis Wise gave goalkeeper Andy Marshall, 29, a new contract in the summer and wants him to fight it out with the Republic of Ireland Under-21 international.
Stack knew he would have stiff competition again but was attracted by the challenge of being involved in a promotion push and a UEFA Cup campaign.
"I am confident in my own ability and the competition will help me," he said.
Stack got the nod for Millwall's goalless Championship opener at Plymouth and should start tonight against Wigan at The Den.
Winger Paul Ifill will be missing and could be out for up to three weeks with an Achilles injury. Midfielder Adrian
Serioux, 25, should sign today but will not be available to play against Wigan.
The Canadian impressed against Wise's side during their pre-season tour and is available on a free from Toronto Lynx.
He follows last week's signing of Josh Simpson from Canada.