Morrell received his education at the University of New Orleans and the Loyola University New Orleans College of Law, dates missing.
Morrell and his wife, Cynthia Hedge-Morrell, a member from 2005 to 2014 of the New Orleans City Council, have four sons. Two, Todd and Nicholas Morrell, are officers of the New Orleans Police Department. Jean-Paul Morrell in 2006 succeeded his father as state representative and in 2009 entered the Louisiana State Senate, where he still represents District 3 in the upper chamber. Arthur and Jean-Paul Morrell operate Morrell & Morrelle, LLC, in New Orleans. He also has 11 grandchildren. Kristen, Farrah, Ana, Mea, Maximillan, Dysen, Jude, Fiona, Alis, Alexander, and Alivia Morrell. He also has one great grandchild Sa'Niyah.
He has also resided in Baton Rouge, Prairieville in Ascension Parish, Mandeville in St. Tammany Parish, Newark, Delaware, and Indianapoliys, Indiana, dates unavailable.
In the nonpartisan blanket primary in October 1983, Morrell forced incumbent Democrat George C. "Nick" Connor, Jr., into a runoff election for the District 97 House seat. Connor nearly won outright with 5,032 votes (49.3 percent). Morrell, who enjoyed strong support from then-mayor Ernest N. Morial and in turn supported Morial's ultimately failed bid to change the city charter to allow him to serve unlimited terms as mayor, trailed with 4,009 (39.3 percent). Democrat Julius Green held the remaining vote, 1,164 (11.4 percent). In the second balloting, Morrell upset Connor by 56 votes, 3,276 (50.4 percent) to 3,220 (49.6 percent).
Morrell was unopposed for his second House term in 1987 and won handily for his third term in 1991, when he defeated fellow Democrat Donald Ray Pryor, 7,131 (66.3 percent) to 3,618 (33.7 percent). Two intra-party rivals held Morrell to 59.7 percent in the 1995 primary. His tally increased to 76 percent in the 1999 primary. In his last House race in 2003, Morrell defeated fellow Democrat Andre Haydel, 6,747 (65 percent) to 3,628 (35 percent).
In 2004, Morrell polled 47,222 votes (2.6 percent) in therace for the United States Senate seat vacated by the Democrat John Breaux. Victory went to then U.S. Representative David Vitter, a Republican from Louisiana's 1st congressional district. Vitter held the seat until 2017 and was a 2015 candidate for governor of Louisiana.
In 2006, Representative Morrell was elected Criminal Clerk of Court in a runoff election with his fellow Democrat, Nick Varrecchio. Morrell polled 60,828 votes (58.05 percent) to Varrecchio's 43,960 (42.05 percent). Morrell had led Varrecchio by four percentage poinst in the primary. Nine other candidates, including two Republicans, were eliminated in the primary.
He then resigned his House seat, and his son, Jean-Paul, won the special election to succeed his father.
In 2010, Morrell won in a landslide for his second term as criminal court clerk. He polled 63,827 votes (82 percent) to the No-Party candidate, Harold E. Wieser, who drew 14,021 (18 percent). In 2014, Morrell scored his third term as criminal clerk, with 56,626 votes (72.4 percent) to 21,595 (27.6 percent) for the No Party candidate, Robbie Keen. While Morrell was reelected as criminal clerk in 2014, his wife was defeated in her bid for an at-large seat on the city council.
In 2014, Morrell clashed with Stacy Head, the city council president, over the budget for the criminal court, which is mandated under the Louisiana Constitution but financed by the municipality. Head halted Morrell from presenting his 2015 budget figures because he did not have the information in a required standardized format, whereas other department heads followed the protocol. Morrell has also been in disagreement with Mayor Mitch Landrieu since 2012 over how much authority the city maintains over Morrell's budget. The Louisiana Court of Appeal for the Fourth Circuit has declared that though the city has authority over the court budget, it must be "fully funded" under state law.