Discovery landed at Edwards Air Force Base at around 1312 BST (0512 PST; 1212 GMT) when bad weather forced a change to the intended Florida landing site.
Columbia broke up on re-entry because of damage it sustained when foam debris fell off the fuel tank during lift-off.
On leaving Discovery, the crew went to inspect the vehicle on the tarmac.
“It’s absolutely fantastic to be back on planet Earth,” said Discovery’s commander Eileen Collins at a post-landing press conference on Tuesday.
But the first woman to command a shuttle mission added that the crew had experienced mixed feelings: “It’s a very bittersweet day for us too. We remember the Columbia crew and their families.
She added: “Our heart goes out to them as we reach a point of closure.”
Nasa officials cheered and clapped as Commander Collins made a perfect landing on runway 22 at Edwards Air Force Base about 54 minutes before dawn.
The shuttle touched down at around 322km/h (200mph), deploying its parachute to slow its speed after making a 196-degree turn to align itself with the landing strip. Its steep trajectory took it over the Pacific Ocean and just north of Los Angeles.
“It’s going to be really hard to top this mission,” Nasa’s administrator Mike Griffin told reporters at a post-launch news briefing at Kennedy Space Center in Florida, “The crew performed fantastically well.”
SHUTTLE LANDING SITES
Kennedy Space Center – the shuttle’s “home” and preferred site for landing
Edwards Air Force Base – the shuttle has landed a total of 50 times at the base
White Sands – back-up known as Northrup Strip lies 45 miles north of US Army missile range
But the mission was not a complete success. As with Columbia, foam debris broke free from Discovery’s external tank during launch. On of these chunks of foam was only slightly smaller than the one that doomed Columbia and Nasa has grounded its shuttle fleet until the problem is fixed.
Officials wouldn’t be drawn on when the shuttle mission – still officially slated for September – might be able to launch.
“Until we get some data back, we can’t make that decision. We will fly it when it’s ready to go,” said the shuttle programme manager Bill Parsons.
Astronaut Steve Robinson also had to conduct an audacious spacewalk to remove two cloth gap fillers which were sticking out from beneath the vehicle.
“This is a difficult and risky endeavour,” said flight director LeRoy Cain, adding: “If it was easy everyone would be doing this.”
Commander Collins made an open plea for people to support the shuttle and Nasa’s programme of space exploration: “Some people say we should stop flying the shuttle because we’ve had an accident – frankly two accidents – but we are people who believe in this mission and we’re going to continue it.
“I ask you to please support it it’s very important to us…space exploration is a fantastic part of the human experience.”
Eileen Collins talks to astronaut Andy Thomas after landing
At 1206 BST (0706 EST; 1106 GMT) on Tuesday, the orbiting shuttle began its return to Earth by firing its two Orbital Manoeuvring System engines for about two minutes 42 seconds at an altitude of around 329km (205 miles).
The shuttle started to experience the burning effects of the atmosphere at about 120km (75 miles) and a speed of about 27,360km/h (17,000mph), pitching down and then up so the protected underside was exposed to the most intense heating.
Under certain circumstances, the shuttle’s belly can be subjected to temperatures of 1,600C (3,000F) – hot enough to melt steel. Five minutes after hitting the atmosphere, Discovery began the first of four banks from side to side in order to lose speed.
Nasa will spend about $1m on returning the shuttle from California to Florida where its launches take place. It should be back at Kennedy Space Center in nine or 10 days.
Edwards Air Force Base was the second choice landing site. Rainstorms and lightning within 30 nautical miles (55.6km) of the Kennedy Space Center – the shuttle’s “home” – forced Nasa to scrub the two available landing opportunities in Florida on Tuesday.
The situation aboard the shuttle meant Nasa were keen to bring Discovery down today.
The crew only had enough consumables, such as food and water, to take them through Wednesday. The shuttle’s ability to remove carbon dioxide gas from the crew decks was also due to run down after Wednesday.
Discovery was due to land on Monday in Florida but bad visibility due to a deck of low-lying cloud forced a delay for 24 hours.