Cockbain, 31, will join the Blues' Celtic League squad next week on a short-term contract that will make him available until the beginning of April.
Coach David Young said: "When a player of Matt's pedigree and experience becomes available you have to sit up and take notice. We certainly did and the result is a valuable addition to our playing resources for the next couple of months. With Dan Baugh suspended and Martyn Williams away on Six Nations' duty, we were likely to be short of cover in the back row. Now we have another world-class flanker on board at a time when we play several crucial Celtic League fixtures."
Cockbain, who is 6'5" tall and weighs in at around 17 stones, is set to arrive in Cardiff next week. He was a member of Australia's World Cup-winning team at the Millennium Stadium in 1999, played in all three tests against the Lions in 2001, and his six appearances in last year's World Cup took his international cap total to 63.
Madden, 30, returns to the Cardiff club where he played all his youth rugby. A product of Cardiff Schools' Rugby Union, he first played at fly-half for Cardiff under-11s,then switched to Number 8 while at St Illtyd's College and, finally, as a prop won representative honours for Wales under-15 and Wales Youth.
Spells of senior rugby with Pontypool and Penzance were followed by nearly six seasons at Llanelli during which he won Welsh Cup medals, played in 29 Heineken Cup ties, and gained five international caps.
Having completed his registration today, he said: "It's great to return to my roots and play again at the Arms Park where I have many happy memories. I'm looking forward to the Premier Division games with the Blue & Blacks for the rest of the season but I still have longer term ambitions. When I'm really up and running my sights will firmly be on a regional contract with the Blues. I reckon I have at least four years of top-class rugby left in me."
Coach Mike Rayer is hoping to involve Madden in the preparations for Cardiff's away fixture at Newbridge on Saturday 31 January.
But the bad news for the Blues is that, with Cardiff already eliminated from the Heineken Cup this season, neither player will represent the Regional outfit in Europe's premier competition.
And, under an agreement reached between the WRU and ERC, the worst peforming Welsh region will compete in next year's Parker Pen Competition.
WIth Cardiff having recorded just one win so far this year, there is a strong chance they may be the side that competes in the second teir next year.