ZTE Corp's deal with state-run operator Ethio Telecom was signed in 2013. The other half of the overall a $1.6 billion package to help double mobile subscribers was shared with another Chinese firm, Huawei Technologies Co Ltd.
But Ethiopian and ZTE differed over the cost of upgrading an existing network. Ethiopian officials said the firms were expected to carry out the upgrade at no extra charge, while ZTE said it would cost an additional $150 million to $200 million.
Ethiopian officials had said Nokia and Ericsson could take some work if agreement was not reached.
Ethio Telecom Chief Executive Andualem Admassie told Reuters that discussions with Ericsson were nearing completion.
"Ericsson will start working on that share of expansion work," he said, without giving a value for the deal. "We are only waiting for confirmation from the (Ethio Telecom) board."
"Huawei is continuing its role," he said, adding that ZTE would continue with some work. "ZTE have lost parts of their share but have made it clear they are willing to resume work, no matter what the current circumstances."
Ericsson could not immediately be reached for comment.
The overall project aims to help the nation of more than 90 million people double mobile subscribers to 50 million in the next year and expand its 3G service.
The overall contract also includes a plan for Huawei to roll out a high-speed 4G network in Addis Ababa.
China has extended its economic influence in Africa in recent years, with state-owned firms winning road tenders in Kenya, signing deals for construction of energy projects in Uganda and running mining projects in various countries.
The $1.6 billion contract signed with the Chinese firms in Ethiopia had a long-term loan package to be paid over a 13-year period with interest of less than 1 percent, officials said.