Alierta, 70, proposed the company's chief operating officer Jose Maria Alvarez-Pallete, 52, as his replacement, Telefonica said in a statement. Alierta will remain on the company's board.
The former financial analyst took over as chairman of Telefonica in 2000 having previously overseen the transformation of Spain's state tobacco company Tabacalera SA, now a subsidiary of Imperial Tobacco, into a private company.
Boosted by a decade-long boom in its domestic market before the global financial crisis hit in 2007, under Alierta's watch Telefonica pushed into new markets across Europe and Latin America.
The company spent over €100 billion ($90 billion) in acquisitions and capital investment between 2000 and 2015, according to Telefonica's own calculations.
In recent years the heavily indebted company has retrenched in Europe and has focused on its domestic market and key markets in Latin America such as Brazil, its second-largest area.
Telefonica is the biggest European telecoms investor in Latin America, where it is the largest or second-largest carrier in most markets.
The company is waiting for regulatory approval from Brussels for the sale last year of its UK mobile unit, 02, to Hong Kong conglomerate CH Hutchison for 10.25 billion pounds.
Telefonica is now trying to reduce debt, revive its domestic business and reverse shrinking revenue from recession-hit Brazil.
Alierta also spearheaded Telefonica's push into high value services such as fibre optics, Pay TV and 4G.
Telefonica's board will meet April 8th to consider naming Alvarez-Pallete, a marathon runner who has since 2012 worked directly under Alierta while being groomed for the top job.
Analysts said the company would not change strategy under Alvarez-Pallette.
"He is an in house man and he has worked for a long time with Cesar Alierta," said Ivan San Felix, an equity analyst at Renta4 in Madrid.
"He will not change anything in the short term," added Jaime Diez, an equity analyst at XTB in Madrid.
Alvarez-Pallete, who also speaks English, French and Portuguese, joined Telefonica from construction firm Cemex in 1999. He has been chief operating officer since 2012.
Alierta considers Alvarez-Pallete "the most-prepared director to successfully confront the challenges of the digital revolution", Telefonica said in its statement
Telefonica posted a net profit of €2.75 billion ($3.1 billion) in 2015, a 8.5 percent drop from the previous year in part due to costs associated with voluntary redundancies in Spain.
Telefonica shares closed up 1.48 percent at 9.86 euros outperforming the Ibex-35 index of most-traded Spanish shares which finished 0.21 percent higher.
By Laure Fillon