The announcement came as NFL Media reported the NFL Players Association has contacted the agents of Dolphins teammates Richie Incognito and Jonathan Martin to request a meeting. The report said the NFLPA wants union head DeMaurice Smith present at such a meeting, to discuss the reasons Martin left the team and why Incognito was suspended indefinitely for conducted detrimental to the team.
Incognito was suspended after Dolphins' executives received evidence he sent Martin text messages and emails containing abusive and racially offensive messages.
Goodell, in a statement issued by the NFL, said Wells -- a senior partner in the New York law firm of Paul, Weiss, Rifkind, Wharton & Garrison -- will "conduct a thorough and objective investigation. He will ensure that we have all the facts so that we can address this matter constructively."
Goodell said Wells will have "full authority to investigate as he deems appropriate" and the report will be made public.
Wells has conducted similar investigations into sexual harassment in the Syracuse University basketball program and a leadership dispute within the NBA players union.
"Under league policy, all employees have the right to a workplace free of any form of harassment," Goodell said. "We are fully committed to an appropriate working environment for all NFL personnel."
The Dolphins have said they support the investigation, NFL Media reported.
Incognito told WSVN-TV, Fort Lauderdale, Fla., Tuesday he was "just trying to weather the storm right now. This will pass."
The South Florida Sun Sentinel reported Tuesday Dolphins' coaches asked Incognito to toughen up Martin, but Incognito went too far.
Incognito's alleged harassment and bullying of Martin is reported to have begun in April after Martin missed two voluntary practices.
The report said coaches urged Incognito to call Martin to "get him into the fold." In a voice mail, he allegedly called the biracial Martin a "half [expletive]," told him "I'll kill you," and threatened to slap his mother.
Teammates said Incognito enjoyed his role as enforcer.
"Richie is the type of guy where if he's on your team you love him," one player said. "If he's not on your team, you hate him. Every team needs a guy like that."
Martin left the team last week, accusing the Dolphins of having an unsafe work environment.
Notable deaths of 2014 [PHOTOS]