Hammers boss Sam Allardyce moved for the former Birmingham central defender with three of his first-team regulars sidelined through injury.
Winston Reid has been out since early November with an ankle injury and he was joined in the treatment room over Christmas by James Collins (calf) and James Tompkins, who has a groin problem.
Johnson, who has been on loan at Sheffield Wednesday since September, could go straight into the team for Wednesday's Capital One Cup semi-final against Manchester City if his registration is completed in time.
And Wolves manager Kenny Jackett believes the loan deal offers the 30-year-old an ideal opportunity to kickstart his career in the top flight.
"It is just a loan deal at the moment and the finances are structured around him playing, how many appearances he makes and whether they are successful," he told the Express & Star.
"It's a really good opportunity for him because he's going to a Premier League club."
West Ham had previously been linked with Manchester City's Joleon Lescott and Johnny Heitinga of Everton in their quest to ease their injury crisis.
You can see if West Ham can take a step towards a Wembley final live on Sky Sports 1 this Wednesday from 7.00pm