The Falcons selected Jones with the No. 6 overall pick acquired from Cleveland on Thursday night for a package of five draft picks, including Atlanta's No. 27 overall selection in the first round this year and the team's first-round pick in 2012.
The Browns also acquired the Falcons' second- and fourth-round picks this year and fourth-round selections in 2012.
The Falcons will pair the physical Jones with their Pro Bowl receiver Roddy White, giving quarterback Matt Ryan another top target.
"We knew it was going to be an aggressive move and cost us," Dimitroff said. "As an organization we felt very strongly about the move for a player who truly adds the explosive, urgent athleticism we're looking for to improve on this team."
Jones said he was "very shocked" the Falcons made such a big investment to select him in the draft.
"It took me by surprise," Jones said. "I feel like they have a lot of trust in me. I'm not going to disappoint."
Due to the ongoing labor unrest, teams were prevented from including current players in draft-day trades. Dimitroff had the difficult task of using only draft picks to trade up from the No. 27 spot.
"You had to really drill down and become that much more focused on how you're going to put together the compensation package," he said. "It took a lot more conversation that it would have if you had players you could discuss."
Dimitroff said he is confident he has enough depth to overcome losing so many draft picks.
"Our feeling on this again was where we are in the draft, where we are with our team, where we are with our roster, we are still very young," he said. "We have a lot of players we have drafted in the last few years in the middle rounds who are still coming into their own and still developing.
"We felt we needed to make a bold statement as far as an impact-type player and possibly obviously give up some of the picks in the middle rounds. We have a lot of players that satisfy our needs as backups and strong depth players right now so we wanted to go after a guy who would be a serious impact-type player."
Dimitroff said he ranked Jones (6-4, 220) and Georgia's A.J. Green similarly high and would have been happy with either receiver.
The Bengals took Green with the fourth pick.
Many draft experts expected the Falcons to use their first-round pick for a defensive end.
Atlanta tied for 20th in the league with only 31 sacks last season. The team's top pass-rusher, John Abraham, had 13 sacks last season, but he will be 33 next season.
"In my mind the explosiveness we feel we're going to get from Julio outweighed what we felt we were going to get on defense in the first round," Dimitroff said.
Jones entered the draft after leading Alabama with 78 catches for 1,133 yards and seven touchdowns as a junior. He had 179 receptions for 2,653 yards and 15 touchdowns in three seasons while starting in each of his 40 games.
Jones is regarded as a strong blocker, a strength which had Falcons coach Mike Smith smiling on Thursday night.
"Our wide receivers are going to block and Julio fits that mold," Smith said. "That's one of the skills we really look at.
"Julio is a big, explosive wide receiver who is going to add to the explosiveness of our team. It's something in the offseason as we've been studying, we know we need to be more explosive and it's going to be a very competitive group now at wide receiver."
Jones, from Foley, Ala., said he didn't suffer a personal loss in the storms which tore through his home state on Wednesday. One of the cities hit hard was Tuscaloosa, the home of the University of Alabama.
"I'm going to do what I can to give back to Tuscaloosa because they've been there for me from the start," Jones said, adding "I prayed about it when I heard the news yesterday."
This marks the third time in eight years the Falcons have used a first-round pick on a wide receiver, following Michael Jenkins in 2004 and White in 2005.
Jenkins, at No. 28, and White, at No. 27, were late first-round picks. Jones is the Falcons' highest pick since the team selected Ryan No. 3 overall in the 2008 draft, Dimitroff's first as general manager.
The Falcons still have picks in the third, fifth and sixth rounds, plus three seventh-round selections, in this draft.