Pleased to Meet Me is the only album recorded by the band as a trio. After their previous album Tim, guitarist Bob Stinson either was kicked out of the band (ostensibly for problems with drugs and alcohol, though most of the other Replacements also had serious substance abuse problems at the time) or quit on his own volition due to creative differences. Many have attributed the noticeable shift toward a more accessible American rock and roll sound on Pleased to Meet Me to Bob Stinson's departure. The band recorded the demos for this album in August 1986, while Bob Stinson was still in the band.
While the punk roots of the group were still apparent on Tim, by Pleased to Meet Me they were there more in spirit as the band delved into other genres, such as soul and cocktail jazz, alongside tracks featuring their customary hard rocking sound. Perhaps due to the album's recording in soul music center Memphis, Tennessee, or the influence of producer Jim Dickinson, the band augmented its sound with saxophone on the tracks "I Don't Know" and "Nightclub Jitters" and a horn section on "Can't Hardly Wait", which features Big Star vocalist Alex Chilton on guitar. The lyrics and idea for "IOU" were based on an autograph "IOU nothing" that Iggy Pop had given Westerberg backstage several years earlier.
The album's cover art mocks the band's transition from young punks to successful musicians with a major record deal, depicting a handshake between one person clad in a suit, starched white shirt, glitzy watch and diamond ring and the other wearing a ripped workshirt. The self-mocking tone continues on the song, "I Don't Know", with its chorus, "One foot in the door/The other one in the gutter." The color scheme of the cover art was an homage to the 1960 Elvis Presley album G.I. Blues.
Pleased to Meet Me was acclaimed by music critics. Writing for Rolling Stone, David Fricke described it as "an album alive with the crackle of conflicting emotions and kamikaze rock & roll fire." In a retrospective review, Thomas Erlewine of AllMusic felt that Pleased to Meet Me "was the last time [The Replacements] could still shoot for the stars and seem like their scrappy selves and, in many ways, it was the last true Replacements album". The album appeared at number three in The Village Voice's Pazz & Jop critics' poll for 1987. In 2012, Paste placed the record at number 70 on its list of "The 80 Best Albums of the 1980s".