The 3-point specialist signed a one-year deal for the veteran's minimum, worth approximately $1.2 million, according to a league source.
Kapono, 30, has career averages of 6.9 points and 1.8 rebounds while shooting 43.7 percent from beyond the arc. He led the league in 3-point accuracy in back-to-back seasons, connecting on 51.4 percent for Miami in 2006-07 and 48.3 percent for Toronto in 2007-08.
"I've always wanted to play here," Kapono said earlier this week. "I grew up watching Pat Riley and I wanted to be like James Worthy and Michael Cooper and Magic [Johnson] and all those guys. So, I was always a fan."
Morris, a 6-foot-4, 190-pound point guard, was selected No. 41 overall. He played two seasons at the University of Michigan, averaging 9.9 points, 2.9 rebounds and 4.8 assists for his college career. Last season, as a sophomore, he led the Big Ten Conference in assists with 235.
Terms of Morris' contract were not disclosed.
Goudelock, a 6-foot-3, 200-pound combo guard, was selected with the No. 46 pick. He averaged 18.4 points, 3.3 rebounds and 3.0 assists in four seasons at the College of Charleston. His 23.7 points per game average in his senior season ranked fourth nationally among all NCAA Division 1 players.
Goudelock signed a two-year deal for the rookie minimum, according to his agent, Alston Walton. The first year is non-guaranteed and the Lakers have a team option on the second season.
Center Atek Majok, selected No. 58, is not in camp with the Lakers.
Also Friday, the Lakers signed two D-Fenders, forward Zach Andrews and guard Elijah Millsap.
Dave McMenamin covers the Lakers for ESPNLosAngeles.com. ESPNLosAngeles.com's Land O' Lakers Blog host Brian Kamenetzky contributed to this report.