The 20-year prosecutor said she can continue to be "an effective voice for the people of Massachusetts."
Kennedy died last week of brain cancer at age 77.
Coakley said at a news conference the state has had a "crisis of confidence" following Kennedy's death and she wants to pick up his mantle.
"We've depended on him here in the Commonwealth and in Washington, and we will miss his strength and leadership and his sense of humor. As some have noted, no one can fill his shoes, but we must strive to follow in his footsteps," she told supporters at a downtown Boston hotel.
Coakley sidestepped a question from reporters whether she favored changing state law to allow the governor to appoint an interim senator, as Kennedy had requested in a letter before his death. Legislators have planned a hearing on the matter for next week.
"For me, personally, I am fully focused on the race," she said, adding she trusted legislators "will make the right decision."
The 56-year-old Coakley becomes the most prominent candidate to officially declare. Several others are waiting for Kennedy's nephew, former Rep. Joseph P. Kennedy II, to decide if he will run.
Coakley said in response to a question that she decided to commit to the race without waiting to see whether a Kennedy family member would run because the senator had declared, in his letter seeking an interim appointment, that the state needs strong and effective representation in Washington.
In a follow-up interview with The Associated Press, she said:
Growing up in the Vietnam era has made her wary of President Barack Obama getting dragged into a protracted military engagement in Afghanistan, but "I trust him for now."
She has focused on health care cost containment as attorney general, since Massachusetts has the nation's first universal health insurance law, and is in favor of it being included in any overhaul law the president signs. She also said a so-called "public option" for providing government-sponsored insurance should be considered.
She dismissed as "frivolous" a Massachusetts Republican Party complaint that she used $24,000 in state campaign money to pay Washington-based consultants as she considered a federal campaign. She said all her actions have been in compliance with state and federal ethics laws.
Coakley told her supporters she decided to run "because government should work well and it has to work for everyone," adding that the performance of government "has been in some ways disheartening and discouraging."
"I believe now is the time to move beyond the idea of, well, `It's good enough for government work,' and demand a new standard of excellence. And I know that I need to prove to voters across the commonwealth that I am the best candidate and that I would be the best new senator from Massachusetts," Coakley said.
Coakley described her humble roots in western Massachusetts and her career as a prosecutor, both as Middlesex District Attorney in a large district that includes populous suburbs of Boston, and since, 2007, as the state's attorney general. She briefly teared up and paused as she described how she has reminded her staff to focus on the needs of crime victims.
"Now, with your help, I hope to bring my experience to Washington," Coakley said.
She did not overtly highlight her status as the state's top female elected official. In the interview, she said, "I think that we've reached a time when women are in business, they're in politics, they're in government. They should be. We're still breaking barriers, but I think I've done it on the merits."
Other potential Democratic candidates include U.S. Reps. Michael Capuano and Stephen Lynch. Potential Republican candidates include former Lt. Gov. Kerry Healey and state Sen. Scott Brown.
Former Boston Red Sox pitcher Curt Schilling is considering an independent campaign but told a radio station Thursday that the chances are "slim to none," though he will not rule it out.