Turk declined, and Royals agreed to the contract on Friday.
"We didn't want to wait until Monday and get shut out (from signing a punter)," said Dolphins vice president Rick Spielman. "We felt it was important to get some sort of commitment (Friday), and we did it with Mark. He's experienced. He's a very good directional kicker, and he fits with what we do."
Royals, ironically, was in Dolphins training camp way back in 1989, but was released because the Dolphins also had former Pro Bowler Reggie Roby on the roster.
Since then, Royals has played with Philadelphia, St. Louis, Tampa Bay, Pittsburgh, Detroit and New Orleans. He has averaged 42.3 yards during his career, with a net of 34.5.
Royals struggled last season, averaging only 40.7 yards with a net of 34.2, but he said a leg injury bothered him throughout the season.
In addition to his punting, Royals also is considered a good holder.
His signing came a few days after the Dolphins restructured the contract of defensive tackle Daryl Gardener.
As for Turk, he's not likely to have any problems finding a new job. Among his suitors as the AFC East rival New York Jets and the Minnesota Vikings, who already have signed a couple of former Dolphins players this offseason — defensive ends Kenny Mixon and Lorenzo Bromell.