The deal for the South African-born star was approved by Wales Rugby Union and covers the three years it would take for him to achieve qualification through residency.
And Steenkamp admits he would relish the chance to represent the Red Dragons once he has established himself in the GUINNESS PRO12.
"I'd be delighted," he said.
"As far as I know, the only foreigners that can come to Wales must be eligible to play for Wales in three years' time, so that's why the contract is for three years."
Steenkamp will join the Ospreys second row later this month, after penning a three-year deal to switch from Super Rugby side Stormers.
The pack is looking a little light on experience this season, with Ian Evans and Ryan Jones having departed.
Ospreys assistant coach Gruff Rees was critical of his team's performance in their season-opening 44-13 victory over Treviso.
But Ospreys' forwards coach Chris Gibbes feels Steenkamp's imminent addition is just what is required.
"De Kock will bring aggression, physicality and he's got a good lineout game, good understanding and he's been around the trap and we need that," Gibbes said.
"We could have chucked the young guys out there into the GUINNESS PRO12 and they could have got beaten up and not learned anything.
"We've looked at the development and progression of what these young kids need and this young pack and we've done what we think is the right thing."
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