In her prime-time speech, Ann Romney spoke of her “real marriage” to a steadfast partner and father.
Correspondents say the address aimed to show the human side of the Republican, who lags behind President Barack Obama in likeability ratings.
Mitt Romney will challenge the Democratic president in November’s elections.
Opinion polls show Barack Obama neck and neck with Mitt Romney, who will deliver his big speech to the convention on Thursday.
Highlighting Mitt Romney’s image problem, a new opinion poll suggests the former Massachusetts governor’s favorability rating is the lowest of any major party nominee since Ronald Reagan’s presidency.
Ann Romney, 63, told the audience she wanted to “talk to you from my heart about our hearts”, saying of her husband, “you really should get to know him”.
She talked about the way her husband helped her deal with multiple sclerosis and breast cancer.
“I read somewhere that Mitt and I have a <<storybook marriage>>,” she said.
“Well, in the storybooks I read, there were never long, long rainy winter afternoons in a house with five boys screaming at once. And those storybooks never seemed to have chapters on MS [multiple sclerosis] or breast cancer.
“A storybook marriage? No, not at all. What Mitt Romney and I have is a real marriage.”
She addressed criticism from Democrats over her husband’s successful private equity career.
“Mitt will be the first to tell you that he is the most fortunate man in the world.
“But as his partner on this amazing journey, I can tell you Mitt Romney was not handed success. He built it.”
Ann Romney ended by pledging: “This man will not fail. This man will not let us down.
“He will take us to a better place, just as he took me home safely from that dance.”
Mitt Romney, 65, appeared on stage and kissed his wife as she concluded her remarks, to a standing ovation from the audience.
New Jersey Governor Chris Christie delivered the keynote address after Ann Romney.
“Mitt Romney will tell us the hard truths we need to hear to put us back on the path to growth and create good paying private sector jobs again in America,” he said.
The speeches followed a roll-call of party delegates and a lively voice poll in which state delegates called out their team’s allocation of votes.
Altogether, Mitt Romney secured 2,061 votes, bringing him comfortably over the crucial 1,144 delegates needed to clinch the nomination.
Vice-presidential candidate Paul Ryan was also given the Republican party’s official stamp of approval on Tuesday.
Speakers attacked Barack Obama, with House Speaker John Boehner saying “his record is as shallow as his rhetoric”.
Republican National Committee chairman Reince Priebus said the president has “never run a company. He hasn’t even run a garage sale or seen the inside of a lemonade stand.”
The convention also approved its party platform – a policy agenda that calls for tax cuts to revive the economy, repealing and replacing a healthcare law passed by Barack Obama, and an end to abortion.
Recent opinion polls have indicated that voters view the economy and unemployment, which is stuck at 8.3%, as top priorities.
The platform also calls for the overturning of measures passed to regulate Wall Street in the wake of the 2008 economic collapse.
This is Mitt Romney’s second run for the White House, after an unsuccessful bid in 2008.
President Obama’s re-nomination will be confirmed next week at the Democratic National Convention in Charlotte, North Carolina.
This year’s convention got off to a late start when Monday’s programme was postponed amid concerns that Hurricane Isaac might disrupt the proceedings in Tampa.
But the category one hurricane missed Tampa, instead making landfall in southern Louisiana on Tuesday evening.
It comes almost seven years to the day since Hurricane Katrina devastated New Orleans.
Key convention speeches
Tuesday: Ann Romney, House Speaker John Boehner, South Carolina Governor Nikki Haley, former US senator Rick Santorum, New Jersey Governor Chris Christie
Wednesday: New Mexico Governor Susana Martinez, Arizona Senator John McCain, former Secretary of State Condoleezza Rice, vice-presidential candidate Paul Ryan
Thursday: Former House Speaker Newt Gingrich, former Florida Governor Jeb Bush, Florida Senator Marco Rubio, presidential candidate Mitt Romney
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