All three players were signed before the deadline last Tuesday, meaning official notification had to be in the Commissioner's Office when the clock struck midnight.
The trio will fly to Florida on Wednesday and begin their baseball careers at the team's Spring Training facility in Viera.
Rendon received a four-year deal worth $7.2 million with a club option, according to a baseball source. Rendon has a history of injuries, including a shoulder problem this past season, and spent most of his time at Rice University as a designated hitter.
The muscle strain in the back of his right shoulder didn't appear to slow Rendon's season in 2011. In 63 games, he hit .327 with six home runs, 27 RBIs and a .520 on-base percentage.
Rendon, who will wear No. 23, spent the summer rehabbing the shoulder in Southern California and now says the shoulder is 100 percent.
"I've been throwing the whole summer. There isn't any setbacks from throwing," Rendon said.
Many Draft experts believed that Rendon would be selcted as the second overall pick, but the injury ended up dropping him a few notches. He said he is motivated to prove that he should have been selected higher.
"I try to take everything as a motivation -- whether it be negative or positive about me," Rendon said. "I want to prove them wrong or keep it up when they say positive things about me. I just want to go there and play the best ball."
Rendon will start his professional career at third base, but with Ryan Zimmerman expected to be with the Nationals for years to come, there is a possibility that Rendon may have to make a position switch. He started playing baseball as a shortstop, but the Nationals believe he can play second or first base.
Rendon didn't seem to mind a position switch, but said it was up to the Nationals to make that call.
Meyer, who received a $2 million signing bonus, had a 2.94 ERA and struck out 110 batters in 101 innings for Kentucky this season. Some Draft experts had Meyer taken by the Nationals with the sixth pick, but the team gambled with the hope that he would be available later in the first round, and he was.
"I liked what they did the last couple of years in the Draft," Meyer said. "They've obviously proven that they want to do everything they can to win. A team that is moving in that direction, anybody would want to be a part of it. This is a good team to be on."
Meyer's fastball is typically clocked between 94 and 97 mph. He can throw a knuckle curveball and is developing a changeup, but he needs to improve his command in order to make it to the big leagues.
"The main thing is, I still have command that I have to work on, and that was a lot better at the end of the year," Meyer said.
Goodwin, a compensation pick, will receive a $3.6 million bonus. He hit .382 with eight home runs, 37 RBIs and 42 runs scored in 47 games with Miami Dade College in 2011. The left-handed-hitting Goodwin also posted a .492 on-base percentage and added 16 stolen bases for the Sharks. The Nationals are hoping Goodwin becomes a leadoff hitter in the future.
"I come to the ballpark to play every day," he said. "I'm a competitor, I'm very aggressive and I just enjoy the game."
While waiting to be signed, Goodwin went to summer school and was planning to go to the University of South Carolina and become a business major. He said he will continue his education at his mother's request.
"My mom will stay on me," Goodwin said. "She'll get on me until I go back -- whether I'm 25 or 65."
Bill Ladson is a reporter for MLB.com and writes an MLBlog, All Nats All the time He also could be found on Twitter @WashingNats. This story was not subject to the approval of Major League Baseball or its clubs.