Darvish and fellow starter Matt Harrison threw back-to-back bullpen sessions. Darvish will start on opening day on March 31 against Philadelphia and Harrison started the 2013 opener for Texas.
Darvish, who led the American League with 277 strikeouts last year, threw to minor league catcher Jose Felix.
"Outstanding bullpen, spotting his fastball, had good bite on his breaking ball, threw the ball well," Rangers manager Ron Washington said. "That's the report I got."
After Darvish threw in front of a flock of Japanese media and photographers, Harrison took the mound. The left-hander won 18 games in 2012, but was restricted to two starts last year due to back problems and thoracic outlet surgery on his non-throwing shoulder.
"As far as Harrison goes, I just want him to get out of here healthy," Washington said.
Derek Holland, the only Rangers starter who did not go on the disabled list last season, likely will miss the first half of the season after Jan. 10 knee surgery. Holland, who led Texas with 213 innings in 2013, is still on crutches and not in camp.
"You're talking about a guy for the last four or five years that's been a horse for us as far as innings go," Washington said. "It's a big blow, but it's part of baseball in the area of adversity. We'll get through it.
"One thing we feel like we have here is depth in our pitching. That means someone has to step up. When I heard the news about Derek, the only thing I thought about was getting him well and having him for later on in the year. Losing a Derek Holland, you're losing a ton of innings. It will be nice to have Derek back when he does return."
The Rangers were ravaged by injuries last season and finished second to Oakland for the second straight year in the AL West standings. They tied Tampa Bay for the final wild-card berth, but then lost a one-game playoff to the Rays.
"Just staying healthy, that's the one question I have," Washington said. "If we stay healthy, I like what we have. I just want us to stay healthy. We'll figure the rest of it out."
Colby Lewis, who started the 2012 opener but did not pitch last year after having hip surgery, reported to camp and went out to play catch.
"Let's go get this chicken wing loose," said Lewis, who will throw batting practice Monday.
When it comes to the bullpen, Texas is looking for a closer after Joe Nathan signed a free-agent deal with Detroit. Washington mentioned Neftali Feliz, who logged 72 saves in 2010-11 but was limited to 4 2-3 innings last year after Tommy John surgery, and Joakim Soria, who has 160 career saves, as candidates that "did it before." He also said Tanner Scheppers was a possibility.
"We'll let it play out," Washington said. "We've got options."