The documents unsealed Friday after a request by The Associated Press also tie Rudolph's handwriting to several letters claiming responsibility for other bombings in Alabama and Georgia.
In addition, a statement from a sibling included in the court file says Rudolph speculated, shortly after the 1995 Oklahoma City bombing, that the Olympics would be a prime target for a terrorist attack because the whole world would be watching.
"Rudolph said something to the effect of 'Yeah, something like the Olympics,"' FBI special agent Tracey North wrote in the previously sealed affidavit.
The documents say fibers on the bombs match material taken from Rudolph's truck, and five shell casings found in a storage locker belonging to him contained powder chemically consistent with debris from the Olympic bomb.
The 911 call was received minutes before the bomb exploded in Atlanta's Centennial Olympic Park. The documents say 15 acquaintances listened to the tape and said the caller sounded like Rudolph.
A call after business hours seeking comment from Richard Jaffe, Rudolph's Birmingham lawyer, was not immediately returned.
Jaffe told The Atlanta Journal-Constitution that it was difficult to comment on something he had not seen. "But what you are reading is a document for the purpose of finding probable cause," he said. "You haven't seen any scientific documents or scientific testing.
"So we'll have to see what we find when we have our own experts who aren't employed by the government examine what they have," Jaffe said.
Rudolph, 36, a former soldier and survivalist, was taken into custody last Saturday in the same wilderness region of North Carolina where he long was suspected of living on the lam.
He remains jailed in Birmingham, Ala. He has pleaded innocent in the Jan. 29, 1998, bombing of an abortion clinic that killed an off-duty police officer and critically injured a nurse.
Rudolph is also accused in the 1996 Olympic park bombing in Atlanta, where a woman was killed and more than 100 were injured, and a pair of 1997 bombings in Atlanta at a lesbian bar and a building that housed an abortion clinic.
The documents released Friday say police found cotton fibers on the Atlanta bomb debris, as well as on letters claiming responsibility for the blasts and in Rudolph's truck. Tests showed all the fibers likely came from the same inexpensive, brown work gloves.
The documents say a wooden dowel was inserted like a handle across the top of the backpack Rudolph allegedly used to carry the Olympic bomb. Investigators say the technique was commonly used at the Air Assault School at Fort Campbell, Ky., where Rudolph served in 1988. One soldier told police he saw Rudolph rig his Army pack in the same manner.
Also, all the Atlanta bombs used small Rubbermaid plastic containers and Westclox timers, the documents say. One of the containers was found in a locker Rudolph rented in Murphy, N.C.
Authorities previously said they found nails like those used in the clinic bombs in the locker.
Four letters received by authorities said the Birmingham bombing and both 1997 Atlanta bombings were carried out by the shadowy Army of God, an anti-abortion group. The documents say the handwriting on the letters was very similar to Rudolph's.